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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 15500.</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 15500.</p>
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<h2>What is the Square Root of 15500?</h2>
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<h2>What is the Square Root of 15500?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 15500 is not a<a>perfect square</a>. The square root of 15500 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √15500, whereas (15500)(1/2) in the exponential form. √15500 ≈ 124.496, 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>. 15500 is not a<a>perfect square</a>. The square root of 15500 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √15500, whereas (15500)(1/2) in the exponential form. √15500 ≈ 124.496, 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 15500</h2>
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<h2>Finding the Square Root of 15500</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 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 long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ol><li>Prime factorization method</li>
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<ol><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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</ol><h2>Square Root of 15500 by Prime Factorization Method</h2>
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</ol><h2>Square Root of 15500 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 15500 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 15500 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 15500 Breaking it down, we get 2 x 2 x 5 x 5 x 5 x 31: 22 x 53 x 311</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 15500 Breaking it down, we get 2 x 2 x 5 x 5 x 5 x 31: 22 x 53 x 311</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 15500. The second step is to make pairs of those prime factors. Since 15500 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 15500. The second step is to make pairs of those prime factors. Since 15500 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 15500 using prime factorization is impossible.</p>
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<p>Therefore, calculating 15500 using prime factorization is impossible.</p>
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<h2>Square Root of 15500 by Long Division Method</h2>
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<h2>Square Root of 15500 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<a>square root</a>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<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 15500, we need to group it as 00 and 155.</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 15500, we need to group it as 00 and 155.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1 - 1, 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 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1 - 1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 55, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1; we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 55, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1; we get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 2n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 2n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 55; let us consider n as 2, now 2 x 2 x 2 = 8.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 55; let us consider n as 2, now 2 x 2 x 2 = 8.</p>
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<p><strong>Step 6:</strong>Subtract 55 from 8; the difference is 47, and the quotient is 12.</p>
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<p><strong>Step 6:</strong>Subtract 55 from 8; the difference is 47, and the quotient is 12.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4700.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4700.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 249 because 249 x 9 = 2241.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 249 because 249 x 9 = 2241.</p>
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<p><strong>Step 9:</strong>Subtracting 2241 from 4700, we get the result 2459.</p>
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<p><strong>Step 9:</strong>Subtracting 2241 from 4700, we get the result 2459.</p>
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<p><strong>Step 10:</strong>Now the quotient is 124.4</p>
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<p><strong>Step 10:</strong>Now the quotient is 124.4</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 √15500 is approximately 124.5.</p>
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<p>So the square root of √15500 is approximately 124.5.</p>
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<h2>Square Root of 15500 by Approximation Method</h2>
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<h2>Square Root of 15500 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 15500 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 15500 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √15500. The smallest perfect square of 15500 is 14400, and the largest perfect square of 15500 is 16900. √15500 falls somewhere between 120 and 130.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √15500. The smallest perfect square of 15500 is 14400, and the largest perfect square of 15500 is 16900. √15500 falls somewhere between 120 and 130.</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 (15500 - 14400) ÷ (16900 - 14400) = 0.44.</p>
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<p>Going by the formula (15500 - 14400) ÷ (16900 - 14400) = 0.44.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>Using the formula, we identified the<a>decimal</a>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 120 + 0.44 = 120.44, so the square root of 15500 is approximately 124.5.</p>
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<p>The next step is adding the value we got initially to the decimal number, which is 120 + 0.44 = 120.44, so the square root of 15500 is approximately 124.5.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 15500</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 15500</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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 the square root, like forgetting about the negative square root, skipping long division methods, etc. 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 √15000?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √15000?</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 15000 square units.</p>
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<p>The area of the square is 15000 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 = side2.</p>
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<p>The area of the square = side2.</p>
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<p>The side length is given as √15000.</p>
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<p>The side length is given as √15000.</p>
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<p>Area of the square = side2 = √15000 x √15000 = 15000.</p>
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<p>Area of the square = side2 = √15000 x √15000 = 15000.</p>
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<p>Therefore, the area of the square box is 15000 square units.</p>
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<p>Therefore, the area of the square box is 15000 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 15500 square feet is built; if each of the sides is √15500, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 15500 square feet is built; if each of the sides is √15500, 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>7750 square feet.</p>
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<p>7750 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 15500 by 2 = we get 7750.</p>
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<p>Dividing 15500 by 2 = we get 7750.</p>
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<p>So half of the building measures 7750 square feet.</p>
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<p>So half of the building measures 7750 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 √15500 x 5.</p>
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<p>Calculate √15500 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>622.48</p>
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<p>622.48</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 15500, which is approximately 124.5.</p>
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<p>The first step is to find the square root of 15500, which is approximately 124.5.</p>
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<p>The second step is to multiply 124.5 with 5. So 124.5 x 5 = 622.48.</p>
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<p>The second step is to multiply 124.5 with 5. So 124.5 x 5 = 622.48.</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 (15000 + 500)?</p>
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<p>What will be the square root of (15000 + 500)?</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 124.496.</p>
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<p>The square root is approximately 124.496.</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 (15000 + 500). 15000 + 500 = 15500, and then √15500 ≈ 124.496.</p>
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<p>To find the square root, we need to find the sum of (15000 + 500). 15000 + 500 = 15500, and then √15500 ≈ 124.496.</p>
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<p>Therefore, the square root of (15000 + 500) is approximately ±124.496.</p>
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<p>Therefore, the square root of (15000 + 500) is approximately ±124.496.</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 √15000 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √15000 units and the width ‘w’ is 38 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 approximately 292.992 units.</p>
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<p>We find the perimeter of the rectangle as approximately 292.992 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 × (√15000 + 38) = 2 × (122.474 + 38) ≈ 2 × 160.474 ≈ 320.948 units.</p>
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<p>Perimeter = 2 × (√15000 + 38) = 2 × (122.474 + 38) ≈ 2 × 160.474 ≈ 320.948 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 15500</h2>
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<h2>FAQ on Square Root of 15500</h2>
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<h3>1.What is √15500 in its simplest form?</h3>
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<h3>1.What is √15500 in its simplest form?</h3>
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<p>The prime factorization of 15500 is 2 x 2 x 5 x 5 x 5 x 31, so the simplest form of √15500 ≈ √(2 x 2 x 5 x 5 x 5 x 31).</p>
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<p>The prime factorization of 15500 is 2 x 2 x 5 x 5 x 5 x 31, so the simplest form of √15500 ≈ √(2 x 2 x 5 x 5 x 5 x 31).</p>
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<h3>2.Mention the factors of 15500.</h3>
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<h3>2.Mention the factors of 15500.</h3>
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<p>Factors of 15500 are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 250, 310, 620, 775, 1550, 3100, 7750, and 15500.</p>
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<p>Factors of 15500 are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 250, 310, 620, 775, 1550, 3100, 7750, and 15500.</p>
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<h3>3.Calculate the square of 15500.</h3>
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<h3>3.Calculate the square of 15500.</h3>
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<p>We get the square of 15500 by multiplying the number by itself, that is 15500 x 15500 = 240250000.</p>
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<p>We get the square of 15500 by multiplying the number by itself, that is 15500 x 15500 = 240250000.</p>
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<h3>4.Is 15500 a prime number?</h3>
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<h3>4.Is 15500 a prime number?</h3>
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<p>15500 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>15500 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.15500 is divisible by?</h3>
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<h3>5.15500 is divisible by?</h3>
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<p>15500 has many factors; those are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 250, 310, 620, 775, 1550, 3100, 7750, and 15500.</p>
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<p>15500 has many factors; those are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 250, 310, 620, 775, 1550, 3100, 7750, and 15500.</p>
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<h2>Important Glossaries for the Square Root of 15500</h2>
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<h2>Important Glossaries for the Square Root of 15500</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 42 = 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: 42 = 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 a 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 a principal square root.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares by grouping numbers and performing division step by step.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares by grouping numbers and performing division step by step.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method to estimate the square root of a number by identifying close perfect squares and using a linear approximation formula.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method to estimate the square root of a number by identifying close perfect squares and using a linear approximation formula.</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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<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>