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2026-01-01
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2026-02-28
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<p>276 Learners</p>
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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 15300.</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 15300.</p>
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<h2>What is the Square Root of 15300?</h2>
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<h2>What is the Square Root of 15300?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 15300 is not a<a>perfect square</a>. The square root of 15300 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √15300, whereas (15300)(1/2) in the exponential form. √15300 ≈ 123.693, 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>. 15300 is not a<a>perfect square</a>. The square root of 15300 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √15300, whereas (15300)(1/2) in the exponential form. √15300 ≈ 123.693, 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 15300</h2>
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<h2>Finding the Square Root of 15300</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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<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 15300 by Prime Factorization Method</h2>
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</ol><h2>Square Root of 15300 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 15300 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 15300 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 15300 Breaking it down, we get 2 × 2 × 3 × 5 × 5 × 3 × 17: 2² × 3² × 5² × 17</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 15300 Breaking it down, we get 2 × 2 × 3 × 5 × 5 × 3 × 17: 2² × 3² × 5² × 17</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 15300. The second step is to make pairs of those prime factors. Since 15300 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 15300. The second step is to make pairs of those prime factors. Since 15300 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely.</p>
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<p>Therefore, calculating 15300 using prime factorization is possible but will not result in a perfect integer.</p>
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<p>Therefore, calculating 15300 using prime factorization is possible but will not result in a perfect integer.</p>
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<h2>Square Root of 15300 by Long Division Method</h2>
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<h2>Square Root of 15300 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 15300, we need to group it as 15 and 300.</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 15300, we need to group it as 15 and 300.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 15. We can say n is ‘3’ because 3 × 3 is 9, which is closest to 15. Now the<a>quotient</a>is 3, and after subtracting 9 from 15, 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 closest to 15. We can say n is ‘3’ because 3 × 3 is 9, which is closest to 15. Now the<a>quotient</a>is 3, and after subtracting 9 from 15, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Now let us bring down 300, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 300, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 60. Now we need to find a digit x such that 60x × x is<a>less than</a>or equal to 630. Let's consider x as 1, so 601 × 1 = 601.</p>
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<p><strong>Step 4:</strong>The new divisor will be 60. Now we need to find a digit x such that 60x × x is<a>less than</a>or equal to 630. Let's consider x as 1, so 601 × 1 = 601.</p>
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<p><strong>Step 5:</strong>Subtracting 601 from 630, the difference is 29, and the quotient is 31.</p>
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<p><strong>Step 5:</strong>Subtracting 601 from 630, the difference is 29, and the quotient is 31.</p>
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<p><strong>Step 6:</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 2900.</p>
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<p><strong>Step 6:</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 2900.</p>
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<p><strong>Step 7:</strong>Now we need to find the new digit y such that 620y × y is less than or equal to 2900. Let's consider y as 4, so 6204 × 4 = 24816.</p>
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<p><strong>Step 7:</strong>Now we need to find the new digit y such that 620y × y is less than or equal to 2900. Let's consider y as 4, so 6204 × 4 = 24816.</p>
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<p><strong>Step 8:</strong>Subtracting 24816 from 29000, we get the result 4184.</p>
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<p><strong>Step 8:</strong>Subtracting 24816 from 29000, we get the result 4184.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get the required number of decimal places or until the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get the required number of decimal places or until the remainder is zero.</p>
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<p>So the square root of √15300 is approximately 123.693.</p>
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<p>So the square root of √15300 is approximately 123.693.</p>
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<h2>Square Root of 15300 by Approximation Method</h2>
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<h2>Square Root of 15300 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots, and 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 15300 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots, and 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 15300 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √15300. The smallest perfect square less than 15300 is 14400, and the largest perfect square less than 15300 is 15625. √15300 falls somewhere between 120 and 125.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √15300. The smallest perfect square less than 15300 is 14400, and the largest perfect square less than 15300 is 15625. √15300 falls somewhere between 120 and 125.</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). Going by the formula (15300 - 14400) ÷ (15625 - 14400) = 0.72.</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). Going by the formula (15300 - 14400) ÷ (15625 - 14400) = 0.72.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 120 + 0.72 = 120.72, so the square root of 15300 is approximately 123.693.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 120 + 0.72 = 120.72, so the square root of 15300 is approximately 123.693.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 15300</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 15300</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. 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, such as forgetting about the negative square root or skipping long division steps. 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 √15300?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √15300?</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 15300 square units.</p>
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<p>The area of the square is 15300 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 √15300.</p>
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<p>The side length is given as √15300.</p>
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<p>Area of the square = side² = √15300 × √15300 = 15300.</p>
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<p>Area of the square = side² = √15300 × √15300 = 15300.</p>
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<p>Therefore, the area of the square box is 15300 square units.</p>
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<p>Therefore, the area of the square box is 15300 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 15300 square feet is built; if each of the sides is √15300, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 15300 square feet is built; if each of the sides is √15300, 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>7650 square feet</p>
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<p>7650 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 15300 by 2, we get 7650.</p>
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<p>Dividing 15300 by 2, we get 7650.</p>
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<p>So half of the building measures 7650 square feet.</p>
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<p>So half of the building measures 7650 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 √15300 × 5.</p>
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<p>Calculate √15300 × 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>Approximately 618.465</p>
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<p>Approximately 618.465</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 15300, which is approximately 123.693.</p>
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<p>The first step is to find the square root of 15300, which is approximately 123.693.</p>
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<p>The second step is to multiply 123.693 with 5.</p>
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<p>The second step is to multiply 123.693 with 5.</p>
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<p>So 123.693 × 5 ≈ 618.465.</p>
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<p>So 123.693 × 5 ≈ 618.465.</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 (15200 + 100)?</p>
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<p>What will be the square root of (15200 + 100)?</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 123.693</p>
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<p>The square root is 123.693</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 (15200 + 100). 15200 + 100 = 15300, and then √15300 ≈ 123.693.</p>
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<p>To find the square root, we need to find the sum of (15200 + 100). 15200 + 100 = 15300, and then √15300 ≈ 123.693.</p>
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<p>Therefore, the square root of (15200 + 100) is ±123.693.</p>
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<p>Therefore, the square root of (15200 + 100) is ±123.693.</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 √15200 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 √15200 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>We find the perimeter of the rectangle as approximately 347.386 units.</p>
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<p>We find the perimeter of the rectangle as approximately 347.386 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 × (√15200 + 50) ≈ 2 × (123.491 + 50) ≈ 2 × 173.491 ≈ 346.982 units.</p>
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<p>Perimeter = 2 × (√15200 + 50) ≈ 2 × (123.491 + 50) ≈ 2 × 173.491 ≈ 346.982 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 15300</h2>
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<h2>FAQ on Square Root of 15300</h2>
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<h3>1.What is √15300 in its simplest form?</h3>
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<h3>1.What is √15300 in its simplest form?</h3>
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<p>The prime factorization of 15300 is 2 × 2 × 3 × 3 × 5 × 5 × 17, so the simplest form of √15300 = √(2² × 3² × 5² × 17).</p>
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<p>The prime factorization of 15300 is 2 × 2 × 3 × 3 × 5 × 5 × 17, so the simplest form of √15300 = √(2² × 3² × 5² × 17).</p>
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<h3>2.Mention the factors of 15300.</h3>
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<h3>2.Mention the factors of 15300.</h3>
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<p>Factors of 15300 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 51, 60, 68, 85, 102, 119, 153, 170, 204, 255, 306, 340, 425, 510, 595, 765, 850, 1020, 1275, 1530, 1785, 2550, 3060, 5100, 7650, and 15300.</p>
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<p>Factors of 15300 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 51, 60, 68, 85, 102, 119, 153, 170, 204, 255, 306, 340, 425, 510, 595, 765, 850, 1020, 1275, 1530, 1785, 2550, 3060, 5100, 7650, and 15300.</p>
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<h3>3.Calculate the square of 15300.</h3>
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<h3>3.Calculate the square of 15300.</h3>
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<p>We get the square of 15300 by multiplying the number by itself, that is 15300 × 15300 = 234090000.</p>
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<p>We get the square of 15300 by multiplying the number by itself, that is 15300 × 15300 = 234090000.</p>
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<h3>4.Is 15300 a prime number?</h3>
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<h3>4.Is 15300 a prime number?</h3>
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<p>15300 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>15300 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.15300 is divisible by?</h3>
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<h3>5.15300 is divisible by?</h3>
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<p>15300 has many factors; those include 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 51, 60, 68, 85, 102, 119, 153, 170, 204, 255, 306, 340, 425, 510, 595, 765, 850, 1020, 1275, 1530, 1785, 2550, 3060, 5100, 7650, and 15300.</p>
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<p>15300 has many factors; those include 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 51, 60, 68, 85, 102, 119, 153, 170, 204, 255, 306, 340, 425, 510, 595, 765, 850, 1020, 1275, 1530, 1785, 2550, 3060, 5100, 7650, and 15300.</p>
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<h2>Important Glossaries for the Square Root of 15300</h2>
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<h2>Important Glossaries for the Square Root of 15300</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 method used to find the square root of non-perfect square numbers by dividing the number into groups and finding successive approximations.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect square numbers by dividing the number into groups and finding successive approximations.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to estimate the square root of a non-perfect square by using nearby perfect squares and linear interpolation.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to estimate the square root of a non-perfect square by using nearby perfect squares and linear interpolation.</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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<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>