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2026-01-01
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2026-02-28
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<p>268 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1552.</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, finance, etc. Here, we will discuss the square root of 1552.</p>
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<h2>What is the Square Root of 1552?</h2>
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<h2>What is the Square Root of 1552?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1552 is not a<a>perfect square</a>. The square root of 1552 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1552, whereas (1552)^(1/2) in the exponential form. √1552 ≈ 39.401, 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 of the square of the<a>number</a>. 1552 is not a<a>perfect square</a>. The square root of 1552 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1552, whereas (1552)^(1/2) in the exponential form. √1552 ≈ 39.401, 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 1552</h2>
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<h2>Finding the Square Root of 1552</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<a>long 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<a>long 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 1552 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 1552 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 1552 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 1552 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1552 Breaking it down, we get 2 x 2 x 2 x 2 x 97: 2^4 x 97^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1552 Breaking it down, we get 2 x 2 x 2 x 2 x 97: 2^4 x 97^1</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 1552. The second step is to make pairs of those prime factors. Since 1552 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 1552. The second step is to make pairs of those prime factors. Since 1552 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 1552 using prime factorization is not straightforward for finding the<a>square root</a>.</p>
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<p>Therefore, calculating 1552 using prime factorization is not straightforward for finding the<a>square root</a>.</p>
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<h2>Square Root of 1552 by Long Division Method</h2>
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<h2>Square Root of 1552 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 square root 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 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 1552, we group it as 52 and 15.</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 1552, we group it as 52 and 15.</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 as ‘3’ because 3 x 3 = 9 is<a>less than</a>15. Now the<a>quotient</a>is 3; 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 as ‘3’ because 3 x 3 = 9 is<a>less than</a>15. Now the<a>quotient</a>is 3; after subtracting 9 from 15, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Bring down 52, making the new<a>dividend</a>652. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be part of our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 52, making the new<a>dividend</a>652. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be part of our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n x n ≤ 652. Let us consider n as 9; now 69 x 9 = 621.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n x n ≤ 652. Let us consider n as 9; now 69 x 9 = 621.</p>
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<p><strong>Step 5:</strong>Subtract 621 from 652; the difference is 31, and the quotient is 39.</p>
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<p><strong>Step 5:</strong>Subtract 621 from 652; the difference is 31, and the quotient is 39.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a<a>decimal</a>point, allowing us to add two zeroes to the dividend. The new dividend is 3100.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a<a>decimal</a>point, allowing us to add two zeroes to the dividend. The new dividend is 3100.</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 798 because 798 x 3 = 2394.</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 798 because 798 x 3 = 2394.</p>
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<p><strong>Step 8:</strong>Subtracting 2394 from 3100, we get the result 706.</p>
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<p><strong>Step 8:</strong>Subtracting 2394 from 3100, we get the result 706.</p>
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<p><strong>Step 9:</strong>The quotient is now 39.3.</p>
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<p><strong>Step 9:</strong>The quotient is now 39.3.</p>
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<p><strong>Step 10:</strong>Continue these steps until we have enough decimal places for accuracy.</p>
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<p><strong>Step 10:</strong>Continue these steps until we have enough decimal places for accuracy.</p>
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<p>So, the square root of √1552 ≈ 39.4</p>
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<p>So, the square root of √1552 ≈ 39.4</p>
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<h2>Square Root of 1552 by Approximation Method</h2>
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<h2>Square Root of 1552 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 1552 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 1552 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √1552.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √1552.</p>
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<p>The smallest perfect square less than 1552 is 1521 (39^2) and the largest perfect square more than 1552 is 1600 (40^2).</p>
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<p>The smallest perfect square less than 1552 is 1521 (39^2) and the largest perfect square more than 1552 is 1600 (40^2).</p>
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<p>√1552 falls somewhere between 39 and 40.</p>
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<p>√1552 falls somewhere between 39 and 40.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>(1552 - 1521) / (1600 - 1521) = 31 / 79 ≈ 0.392</p>
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<p>(1552 - 1521) / (1600 - 1521) = 31 / 79 ≈ 0.392</p>
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<p>Using the formula, we identified the decimal.</p>
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<p>Using the formula, we identified the decimal.</p>
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<p>Adding this to our initial<a>whole number</a>gives us 39 + 0.392 = 39.392, so the square root of 1552 ≈ 39.4</p>
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<p>Adding this to our initial<a>whole number</a>gives us 39 + 0.392 = 39.392, so the square root of 1552 ≈ 39.4</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1552</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1552</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 methods. Let us look at a few 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 methods. Let us look at a few 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 √1552?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1552?</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 approximately 1552 square units.</p>
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<p>The area of the square is approximately 1552 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. The side length is given as √1552. Area of the square = (√1552)^2 = 1552. Therefore, the area of the square box is approximately 1552 square units.</p>
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<p>The area of the square = side^2. The side length is given as √1552. Area of the square = (√1552)^2 = 1552. Therefore, the area of the square box is approximately 1552 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 1552 square feet is built; if each side is √1552, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1552 square feet is built; if each side is √1552, 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>776 square feet</p>
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<p>776 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. Dividing 1552 by 2, we get 776. So half of the building measures 776 square feet.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped. Dividing 1552 by 2, we get 776. So half of the building measures 776 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 √1552 x 5.</p>
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<p>Calculate √1552 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>Approximately 197</p>
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<p>Approximately 197</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 1552, which is approximately 39.4. The second step is to multiply 39.4 by 5. So, 39.4 x 5 ≈ 197.</p>
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<p>The first step is to find the square root of 1552, which is approximately 39.4. The second step is to multiply 39.4 by 5. So, 39.4 x 5 ≈ 197.</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 (1552 + 48)?</p>
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<p>What will be the square root of (1552 + 48)?</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 40.</p>
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<p>The square root is approximately 40.</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, calculate the sum of (1552 + 48). 1552 + 48 = 1600, and then √1600 = 40. Therefore, the square root of (1552 + 48) is ±40.</p>
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<p>To find the square root, calculate the sum of (1552 + 48). 1552 + 48 = 1600, and then √1600 = 40. Therefore, the square root of (1552 + 48) is ±40.</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 √1552 units and the width ‘w’ is 48 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √1552 units and the width ‘w’ is 48 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 174.8 units.</p>
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<p>The perimeter of the rectangle is approximately 174.8 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). Perimeter = 2 × (√1552 + 48) ≈ 2 × (39.4 + 48) ≈ 2 × 87.4 ≈ 174.8 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1552 + 48) ≈ 2 × (39.4 + 48) ≈ 2 × 87.4 ≈ 174.8 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 1552</h2>
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<h2>FAQ on Square Root of 1552</h2>
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<h3>1.What is √1552 in its simplest form?</h3>
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<h3>1.What is √1552 in its simplest form?</h3>
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<p>The prime factorization of 1552 is 2 x 2 x 2 x 2 x 97, so the simplest form of √1552 is √(2^4 x 97).</p>
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<p>The prime factorization of 1552 is 2 x 2 x 2 x 2 x 97, so the simplest form of √1552 is √(2^4 x 97).</p>
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<h3>2.Mention the factors of 1552.</h3>
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<h3>2.Mention the factors of 1552.</h3>
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<p>Factors of 1552 are 1, 2, 4, 8, 16, 97, 194, 388, 776, and 1552.</p>
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<p>Factors of 1552 are 1, 2, 4, 8, 16, 97, 194, 388, 776, and 1552.</p>
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<h3>3.Calculate the square of 1552.</h3>
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<h3>3.Calculate the square of 1552.</h3>
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<p>We get the square of 1552 by multiplying the number by itself: 1552 x 1552 = 2,409,904.</p>
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<p>We get the square of 1552 by multiplying the number by itself: 1552 x 1552 = 2,409,904.</p>
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<h3>4.Is 1552 a prime number?</h3>
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<h3>4.Is 1552 a prime number?</h3>
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<h3>5.1552 is divisible by?</h3>
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<h3>5.1552 is divisible by?</h3>
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<p>1552 has several factors; those are 1, 2, 4, 8, 16, 97, 194, 388, 776, and 1552.</p>
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<p>1552 has several factors; those are 1, 2, 4, 8, 16, 97, 194, 388, 776, and 1552.</p>
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<h2>Important Glossaries for the Square Root of 1552</h2>
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<h2>Important Glossaries for the Square Root of 1552</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For 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. For example, 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4. </li>
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<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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<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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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is usually the positive square root that is used, known as the principal square root. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is usually the positive square root that is used, known as the principal square root. </li>
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<li><strong>Prime factorization:</strong>Breaking down a composite number into a product of its prime factors. </li>
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<li><strong>Prime factorization:</strong>Breaking down a composite number into a product of its prime factors. </li>
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<li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.</li>
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<li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.</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>