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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 fields such as vehicle design and finance. Here, we will discuss the square root of 2250.</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 fields such as vehicle design and finance. Here, we will discuss the square root of 2250.</p>
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<h2>What is the Square Root of 2250?</h2>
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<h2>What is the Square Root of 2250?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 2250 is not a<a>perfect square</a>. The square root of 2250 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √2250, whereas in exponential form it is (2250)^(1/2). √2250 ≈ 47.4342, 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 a<a>number</a>. 2250 is not a<a>perfect square</a>. The square root of 2250 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √2250, whereas in exponential form it is (2250)^(1/2). √2250 ≈ 47.4342, 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 2250</h2>
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<h2>Finding the Square Root of 2250</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 typically used for non-perfect square numbers, where<a>long division</a>and approximation methods are more suitable. 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 typically used for non-perfect square numbers, where<a>long division</a>and approximation methods are more suitable. 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 2250 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 2250 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 2250 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 2250 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2250 Breaking it down, we get 2 x 3 x 3 x 5 x 5 x 5: 2^1 x 3^2 x 5^3</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2250 Breaking it down, we get 2 x 3 x 3 x 5 x 5 x 5: 2^1 x 3^2 x 5^3</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 2250. The second step is to make pairs of those prime factors. Since 2250 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 have found the prime factors of 2250. The second step is to make pairs of those prime factors. Since 2250 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 √2250 using prime factorization directly is impractical.</p>
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<p>Therefore, calculating √2250 using prime factorization directly is impractical.</p>
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<h2>Square Root of 2250 by Long Division Method</h2>
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<h2>Square Root of 2250 by Long Division Method</h2>
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<p>The long<a>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<a>square root</a>using the long division method, step by step:</p>
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<p>The long<a>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<a>square root</a>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 2250, we group it as 50 and 22.</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 2250, we group it as 50 and 22.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 22. We can say n as ‘4’ because 4 x 4 = 16, which is less than 22. Now the<a>quotient</a>is 4, and after subtracting 16 from 22, the<a>remainder</a>is 6.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 22. We can say n as ‘4’ because 4 x 4 = 16, which is less than 22. Now the<a>quotient</a>is 4, and after subtracting 16 from 22, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50, making the new<a>dividend</a>650. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50, making the new<a>dividend</a>650. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 8n. We need to find the value of n where 8n x n ≤ 650. Let's consider n as 7; now, 87 x 7 = 609.</p>
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<p><strong>Step 4:</strong>The new divisor will be 8n. We need to find the value of n where 8n x n ≤ 650. Let's consider n as 7; now, 87 x 7 = 609.</p>
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<p><strong>Step 5:</strong>Subtract 609 from 650; the difference is 41. The quotient is now 47.</p>
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<p><strong>Step 5:</strong>Subtract 609 from 650; the difference is 41. The quotient is now 47.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4100.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4100.</p>
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<p><strong>Step 7:</strong>Find a new divisor. Let's estimate 474 x 8 = 3792.</p>
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<p><strong>Step 7:</strong>Find a new divisor. Let's estimate 474 x 8 = 3792.</p>
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<p><strong>Step 8:</strong>Subtract 3792 from 4100; the result is 308.</p>
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<p><strong>Step 8:</strong>Subtract 3792 from 4100; the result is 308.</p>
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<p><strong>Step 9:</strong>Now the quotient is 47.4.</p>
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<p><strong>Step 9:</strong>Now the quotient is 47.4.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we achieve the desired accuracy.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we achieve the desired accuracy.</p>
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<p>So the square root of √2250 ≈ 47.434.</p>
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<p>So the square root of √2250 ≈ 47.434.</p>
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<h2>Square Root of 2250 by Approximation Method</h2>
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<h2>Square Root of 2250 by Approximation Method</h2>
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<p>The approximation method is another technique for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 2250 using the approximation method.</p>
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<p>The approximation method is another technique for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 2250 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around √2250. The closest perfect square below 2250 is 2209, and the one above is 2304. √2250 falls between 47 and 48.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around √2250. The closest perfect square below 2250 is 2209, and the one above is 2304. √2250 falls between 47 and 48.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).</p>
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<p>Using the formula (2250 - 2209) ÷ (2304 - 2209) = 41 ÷ 95 ≈ 0.431.</p>
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<p>Using the formula (2250 - 2209) ÷ (2304 - 2209) = 41 ÷ 95 ≈ 0.431.</p>
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<p>Adding this to the smaller square root: 47 + 0.431 = 47.431.</p>
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<p>Adding this to the smaller square root: 47 + 0.431 = 47.431.</p>
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<p>So, the square root of 2250 is approximately 47.431.</p>
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<p>So, the square root of 2250 is approximately 47.431.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2250</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2250</h2>
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<p>Students often make mistakes when finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>
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<p>Students often make mistakes when finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes 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 √2250?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √2250?</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 2250 square units.</p>
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<p>The area of the square is 2250 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 √2250.</p>
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<p>The side length is given as √2250.</p>
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<p>Area of the square = side^2 = √2250 x √2250 = 2250.</p>
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<p>Area of the square = side^2 = √2250 x √2250 = 2250.</p>
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<p>Therefore, the area of the square box is 2250 square units.</p>
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<p>Therefore, the area of the square box is 2250 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 2250 square feet is built; if each of the sides is √2250, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 2250 square feet is built; if each of the sides is √2250, 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>1125 square feet</p>
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<p>1125 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can simply divide the given area by 2 as the building is square-shaped.</p>
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<p>We can simply divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 2250 by 2 = 1125.</p>
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<p>Dividing 2250 by 2 = 1125.</p>
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<p>So, half of the building measures 1125 square feet.</p>
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<p>So, half of the building measures 1125 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 √2250 x 5.</p>
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<p>Calculate √2250 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>237.17</p>
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<p>237.17</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 2250, which is approximately 47.434.</p>
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<p>The first step is to find the square root of 2250, which is approximately 47.434.</p>
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<p>The second step is to multiply 47.434 by 5.</p>
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<p>The second step is to multiply 47.434 by 5.</p>
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<p>So, 47.434 x 5 = 237.17.</p>
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<p>So, 47.434 x 5 = 237.17.</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 (2250 + 50)?</p>
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<p>What will be the square root of (2250 + 50)?</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 48.9898.</p>
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<p>The square root is approximately 48.9898.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the sum of (2250 + 50) = 2300.</p>
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<p>First, find the sum of (2250 + 50) = 2300.</p>
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<p>Then, find the square root: √2300 ≈ 48.9898.</p>
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<p>Then, find the square root: √2300 ≈ 48.9898.</p>
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<p>Therefore, the square root of (2250 + 50) is approximately ±48.9898.</p>
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<p>Therefore, the square root of (2250 + 50) is approximately ±48.9898.</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 √2250 units and the width ‘w’ is 20 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √2250 units and the width ‘w’ is 20 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>We find the perimeter of the rectangle as 134.8684 units.</p>
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<p>We find the perimeter of the rectangle as 134.8684 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 × (√2250 + 20) = 2 × (47.434 + 20) = 2 × 67.434 = 134.8684 units.</p>
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<p>Perimeter = 2 × (√2250 + 20) = 2 × (47.434 + 20) = 2 × 67.434 = 134.8684 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 2250</h2>
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<h2>FAQ on Square Root of 2250</h2>
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<h3>1.What is √2250 in its simplest form?</h3>
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<h3>1.What is √2250 in its simplest form?</h3>
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<p>The prime factorization of 2250 is 2 x 3 x 3 x 5 x 5 x 5, so the simplest form of √2250 is √(2 x 3^2 x 5^3).</p>
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<p>The prime factorization of 2250 is 2 x 3 x 3 x 5 x 5 x 5, so the simplest form of √2250 is √(2 x 3^2 x 5^3).</p>
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<h3>2.Mention the factors of 2250.</h3>
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<h3>2.Mention the factors of 2250.</h3>
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<p>Factors of 2250 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 250, 450, 750, 1125, and 2250.</p>
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<p>Factors of 2250 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 250, 450, 750, 1125, and 2250.</p>
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<h3>3.Calculate the square of 2250.</h3>
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<h3>3.Calculate the square of 2250.</h3>
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<p>We get the square of 2250 by multiplying the number by itself, that is 2250 x 2250 = 5,062,500.</p>
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<p>We get the square of 2250 by multiplying the number by itself, that is 2250 x 2250 = 5,062,500.</p>
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<h3>4.Is 2250 a prime number?</h3>
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<h3>4.Is 2250 a prime number?</h3>
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<p>2250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>2250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.2250 is divisible by?</h3>
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<h3>5.2250 is divisible by?</h3>
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<p>2250 has many factors; those are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 250, 450, 750, 1125, and 2250.</p>
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<p>2250 has many factors; those are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 250, 450, 750, 1125, and 2250.</p>
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<h2>Important Glossaries for the Square Root of 2250</h2>
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<h2>Important Glossaries for the Square Root of 2250</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. 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 of a square. 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, but the positive square root is often used in practical applications, 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, but the positive square root is often used in practical applications, known as the principal square root.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because 4 x 4 = 16.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because 4 x 4 = 16.</li>
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</ul><ul><li><strong>Division method:</strong>A method used to find the square root of a number by systematically dividing and estimating, such as the long division method.</li>
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</ul><ul><li><strong>Division method:</strong>A method used to find the square root of a number by systematically dividing and estimating, such as the long division method.</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>