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2026-01-01
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2026-02-28
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 45000.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 45000.</p>
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<h2>What is the Square Root of 45000?</h2>
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<h2>What is the Square Root of 45000?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 45000 is not a<a>perfect square</a>. The square root of 45000 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √45000, whereas in exponential form as (45000)^(1/2). √45000 = 212.132, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 45000 is not a<a>perfect square</a>. The square root of 45000 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √45000, whereas in exponential form as (45000)^(1/2). √45000 = 212.132, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 45000</h2>
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<h2>Finding the Square Root of 45000</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method</li>
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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 45000 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 45000 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 45000 is broken down into its prime factors.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 45000 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 45000 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5: 2^3 x 3^2 x 5^4</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 45000 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5: 2^3 x 3^2 x 5^4</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 45000. The second step is to make pairs of those prime factors. Since 45000 is not a perfect square, the digits of the number can’t be completely grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 45000. The second step is to make pairs of those prime factors. Since 45000 is not a perfect square, the digits of the number can’t be completely grouped in pairs.</p>
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<p>Therefore, calculating 45000 using prime factorization involves taking the<a>square root</a>of the product of these pairs.</p>
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<p>Therefore, calculating 45000 using prime factorization involves taking the<a>square root</a>of the product of these pairs.</p>
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<h2>Square Root of 45000 by Long Division Method</h2>
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<h2>Square Root of 45000 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 45000, we need to group it as 00 and 450.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 45000, we need to group it as 00 and 450.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Now we get 4n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>Now we get 4n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 50. Let us consider n as 1, now 4 x 1 x 1 = 4.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 50. Let us consider n as 1, now 4 x 1 x 1 = 4.</p>
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<p><strong>Step 6:</strong>Subtract 50 from 4; the difference is 46, and the quotient is 21.</p>
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<p><strong>Step 6:</strong>Subtract 50 from 4; the difference is 46, and the quotient is 21.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 429 because 429 x 9 = 3861.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 429 because 429 x 9 = 3861.</p>
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<p><strong>Step 9:</strong>Subtracting 3861 from 4600 gives us the result 739.</p>
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<p><strong>Step 9:</strong>Subtracting 3861 from 4600 gives us the result 739.</p>
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<p><strong>Step 10:</strong>Now the quotient is 212.1</p>
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<p><strong>Step 10:</strong>Now the quotient is 212.1</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √45000 is approximately 212.13.</p>
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<p>So the square root of √45000 is approximately 212.13.</p>
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<h2>Square Root of 45000 by Approximation Method</h2>
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<h2>Square Root of 45000 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 45000 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 45000 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √45000. The smallest perfect square less than 45000 is 44100 (210^2), and the largest perfect square<a>greater than</a>45000 is 45369 (213^2). √45000 falls somewhere between 210 and 213.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √45000. The smallest perfect square less than 45000 is 44100 (210^2), and the largest perfect square<a>greater than</a>45000 is 45369 (213^2). √45000 falls somewhere between 210 and 213.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>Going by the formula (45000 - 44100) ÷ (45369 - 44100) = 0.67.</p>
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<p>Going by the formula (45000 - 44100) ÷ (45369 - 44100) = 0.67.</p>
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<p>Using the formula, we identified the decimal point of our square root.</p>
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<p>Using the formula, we identified the decimal point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number, which is 210 + 0.67 = 210.67, so the square root of 45000 is approximately 212.13.</p>
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<p>The next step is adding the value we got initially to the decimal number, which is 210 + 0.67 = 210.67, so the square root of 45000 is approximately 212.13.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 45000</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 45000</h2>
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<p>Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √45000?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √45000?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 45000 square units.</p>
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<p>The area of the square is 45000 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √45000.</p>
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<p>The side length is given as √45000.</p>
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<p>Area of the square = side^2 = √45000 x √45000 = 45000 square units.</p>
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<p>Area of the square = side^2 = √45000 x √45000 = 45000 square units.</p>
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<p>Therefore, the area of the square box is 45000 square units.</p>
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<p>Therefore, the area of the square box is 45000 square units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 45000 square feet is built; if each of the sides is √45000, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 45000 square feet is built; if each of the sides is √45000, what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>22500 square feet</p>
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<p>22500 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 45000 by 2 = we get 22500.</p>
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<p>Dividing 45000 by 2 = we get 22500.</p>
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<p>So half of the building measures 22500 square feet.</p>
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<p>So half of the building measures 22500 square feet.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Calculate √45000 x 5.</p>
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<p>Calculate √45000 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>1060.66</p>
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<p>1060.66</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 45000, which is approximately 212.13.</p>
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<p>The first step is to find the square root of 45000, which is approximately 212.13.</p>
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<p>The second step is to multiply 212.13 by 5.</p>
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<p>The second step is to multiply 212.13 by 5.</p>
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<p>So 212.13 x 5 = 1060.66.</p>
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<p>So 212.13 x 5 = 1060.66.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>What will be the square root of (45000 + 1000)?</p>
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<p>What will be the square root of (45000 + 1000)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 213.6.</p>
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<p>The square root is approximately 213.6.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (45000 + 1000).</p>
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<p>To find the square root, we need to find the sum of (45000 + 1000).</p>
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<p>45000 + 1000 = 46000, and then √46000 ≈ 213.6.</p>
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<p>45000 + 1000 = 46000, and then √46000 ≈ 213.6.</p>
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<p>Therefore, the square root of (45000 + 1000) is approximately ±213.6.</p>
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<p>Therefore, the square root of (45000 + 1000) is approximately ±213.6.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √45000 units and the width ‘w’ is 50 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √45000 units and the width ‘w’ is 50 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 524.26 units.</p>
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<p>The perimeter of the rectangle is approximately 524.26 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√45000 + 50) ≈ 2 × (212.13 + 50) ≈ 2 × 262.13 = 524.26 units.</p>
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<p>Perimeter = 2 × (√45000 + 50) ≈ 2 × (212.13 + 50) ≈ 2 × 262.13 = 524.26 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 45000</h2>
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<h2>FAQ on Square Root of 45000</h2>
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<h3>1.What is √45000 in its simplest form?</h3>
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<h3>1.What is √45000 in its simplest form?</h3>
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<p>The prime factorization of 45000 is 2^3 x 3^2 x 5^4, so the simplest form of √45000 = √(2^3 x 3^2 x 5^4).</p>
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<p>The prime factorization of 45000 is 2^3 x 3^2 x 5^4, so the simplest form of √45000 = √(2^3 x 3^2 x 5^4).</p>
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<h3>2.Mention the factors of 45000.</h3>
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<h3>2.Mention the factors of 45000.</h3>
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<p>Factors of 45000 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 25, 30, 36, 45, 50, 75, 90, 100, 150, 180, 225, 300, 450, 500, 750, 900, 1125, 1500, 2250, 4500, 9000, 15000, and 45000.</p>
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<p>Factors of 45000 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 25, 30, 36, 45, 50, 75, 90, 100, 150, 180, 225, 300, 450, 500, 750, 900, 1125, 1500, 2250, 4500, 9000, 15000, and 45000.</p>
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<h3>3.Calculate the square of 45000.</h3>
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<h3>3.Calculate the square of 45000.</h3>
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<p>We get the square of 45000 by multiplying the number by itself, that is 45000 x 45000 = 2025000000.</p>
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<p>We get the square of 45000 by multiplying the number by itself, that is 45000 x 45000 = 2025000000.</p>
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<h3>4.Is 45000 a prime number?</h3>
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<h3>4.Is 45000 a prime number?</h3>
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<p>45000 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>45000 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.45000 is divisible by?</h3>
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<h3>5.45000 is divisible by?</h3>
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<p>45000 has many factors; it is divisible by numbers including 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450, 500, 750, 900, 1500, 2250, 4500, 9000, 15000, and 45000.</p>
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<p>45000 has many factors; it is divisible by numbers including 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450, 500, 750, 900, 1500, 2250, 4500, 9000, 15000, and 45000.</p>
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<h2>Important Glossaries for the Square Root of 45000</h2>
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<h2>Important Glossaries for the Square Root of 45000</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization of a number is expressing it as a product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization of a number is expressing it as a product of its prime factors.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4^2.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4^2.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>