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2026-01-01
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2026-02-28
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<p>206 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 itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in various fields such as architecture, finance, and engineering. Here, we will discuss the square root of 2548.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in various fields such as architecture, finance, and engineering. Here, we will discuss the square root of 2548.</p>
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<h2>What is the Square Root of 2548?</h2>
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<h2>What is the Square Root of 2548?</h2>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 2548 is not a<a>perfect square</a>. The square root of 2548 can be expressed in both radical and exponential forms. In the radical form, it is written as √2548, whereas in the<a>exponential form</a>it is (2548)^(1/2). The square root of 2548 is approximately 50.4788, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two<a>integers</a>.</p>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 2548 is not a<a>perfect square</a>. The square root of 2548 can be expressed in both radical and exponential forms. In the radical form, it is written as √2548, whereas in the<a>exponential form</a>it is (2548)^(1/2). The square root of 2548 is approximately 50.4788, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two<a>integers</a>.</p>
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<h2>Finding the Square Root of 2548</h2>
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<h2>Finding the Square Root of 2548</h2>
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<p>For perfect square numbers, the<a>prime factorization</a>method is often used. However, for non-perfect square numbers, the<a>long division</a>method and approximation method are more suitable. Let us explore these methods:</p>
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<p>For perfect square numbers, the<a>prime factorization</a>method is often used. However, for non-perfect square numbers, the<a>long division</a>method and approximation method are more suitable. Let us explore these 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 2548 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 2548 by Prime Factorization Method</h2>
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<p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. Let's determine how 2548 is broken down into its prime factors:</p>
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<p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. Let's determine how 2548 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2548 Breaking it down, we get 2 x 2 x 3 x 3 x 71: 2^2 x 3^2 x 71</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2548 Breaking it down, we get 2 x 2 x 3 x 3 x 71: 2^2 x 3^2 x 71</p>
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<p><strong>Step 2:</strong>Having identified the prime factors of 2548, the next step is to pair the factors. Since 2548 is not a perfect square, the factors cannot be fully paired, making the prime factorization approach unsuitable for finding the<a>square root</a>of 2548.</p>
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<p><strong>Step 2:</strong>Having identified the prime factors of 2548, the next step is to pair the factors. Since 2548 is not a perfect square, the factors cannot be fully paired, making the prime factorization approach unsuitable for finding the<a>square root</a>of 2548.</p>
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<h2>Square Root of 2548 by Long Division Method</h2>
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<h2>Square Root of 2548 by Long Division Method</h2>
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<p>The long<a>division</a>method is particularly useful for non-perfect square numbers. This method involves estimating the square root by grouping digits and performing division. Here's how it works step by step:</p>
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<p>The long<a>division</a>method is particularly useful for non-perfect square numbers. This method involves estimating the square root by grouping digits and performing division. Here's how it works step by step:</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits of 2548 from right to left. We group it as 48 and 25.</p>
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<p><strong>Step 1:</strong>Begin by grouping the digits of 2548 from right to left. We group it as 48 and 25.</p>
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<p><strong>Step 2:</strong>Find a number n whose square is closest to 25. In this case, n is 5 because 5 x 5 = 25. Subtract 25 from 25, leaving a<a>remainder</a>of 0.</p>
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<p><strong>Step 2:</strong>Find a number n whose square is closest to 25. In this case, n is 5 because 5 x 5 = 25. Subtract 25 from 25, leaving a<a>remainder</a>of 0.</p>
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<p><strong>Step 3:</strong>Bring down the next group of digits, 48, to form the new<a>dividend</a>, 48.</p>
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<p><strong>Step 3:</strong>Bring down the next group of digits, 48, to form the new<a>dividend</a>, 48.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>(5), making it 10, which becomes the new<a>divisor</a>.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>(5), making it 10, which becomes the new<a>divisor</a>.</p>
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<p><strong>Step 5:</strong>Identify n such that 10n × n is<a>less than</a>or equal to 48. Here, n is 4 because 104 x 4 = 416.</p>
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<p><strong>Step 5:</strong>Identify n such that 10n × n is<a>less than</a>or equal to 48. Here, n is 4 because 104 x 4 = 416.</p>
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<p><strong>Step 6:</strong>Subtract 416 from 480, resulting in a remainder of 64.</p>
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<p><strong>Step 6:</strong>Subtract 416 from 480, resulting in a remainder of 64.</p>
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<p><strong>Step 7:</strong>Add a<a>decimal</a>point to the quotient and bring down two zeros, making the new dividend 6400.</p>
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<p><strong>Step 7:</strong>Add a<a>decimal</a>point to the quotient and bring down two zeros, making the new dividend 6400.</p>
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<p><strong>Step 8:</strong>Determine the new divisor, 1004, where 1004 x 6 = 6024.</p>
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<p><strong>Step 8:</strong>Determine the new divisor, 1004, where 1004 x 6 = 6024.</p>
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<p><strong>Step 9:</strong>Subtract 6024 from 6400, leaving a remainder of 376.</p>
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<p><strong>Step 9:</strong>Subtract 6024 from 6400, leaving a remainder of 376.</p>
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<p><strong>Step 10:</strong>The quotient is 50.4... Continue these steps until the desired precision is reached.</p>
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<p><strong>Step 10:</strong>The quotient is 50.4... Continue these steps until the desired precision is reached.</p>
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<p>The square root of 2548 is approximately 50.48.</p>
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<p>The square root of 2548 is approximately 50.48.</p>
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<h2>Square Root of 2548 by Approximation Method</h2>
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<h2>Square Root of 2548 by Approximation Method</h2>
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<p>The approximation method is another approach to determine square roots, providing a straightforward way to estimate the square root of a given number. Here's how to approximate the square root of 2548:</p>
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<p>The approximation method is another approach to determine square roots, providing a straightforward way to estimate the square root of a given number. Here's how to approximate the square root of 2548:</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 2548. The nearest perfect squares are 2500 and 2601. √2548 falls between 50 and 51.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 2548. The nearest perfect squares are 2500 and 2601. √2548 falls between 50 and 51.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (2548 - 2500) / (2601 - 2500) = 48/101 ≈ 0.475</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (2548 - 2500) / (2601 - 2500) = 48/101 ≈ 0.475</p>
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<p><strong>Step 3:</strong>Add this decimal to the lower integer bound: 50 + 0.475 = 50.475</p>
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<p><strong>Step 3:</strong>Add this decimal to the lower integer bound: 50 + 0.475 = 50.475</p>
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<p>Thus, the square root of 2548 is approximately 50.475.</p>
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<p>Thus, the square root of 2548 is approximately 50.475.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2548</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2548</h2>
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<p>Students may make errors while calculating square roots, such as neglecting the negative square root or improperly applying the long division method. Let's explore some common mistakes in detail.</p>
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<p>Students may make errors while calculating square roots, such as neglecting the negative square root or improperly applying the long division method. Let's explore some common 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 √2548?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √2548?</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 2548 square units.</p>
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<p>The area of the square is 2548 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 a square is calculated as side^2.</p>
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<p>The area of a square is calculated as side^2.</p>
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<p>Given the side length as √2548.</p>
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<p>Given the side length as √2548.</p>
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<p>Area = (√2548) x (√2548)</p>
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<p>Area = (√2548) x (√2548)</p>
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<p>= 2548</p>
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<p>= 2548</p>
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<p>Therefore, the area of the square box is 2548 square units.</p>
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<p>Therefore, the area of the square box is 2548 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 2548 square feet is built; if each of the sides is √2548, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 2548 square feet is built; if each of the sides is √2548, 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>1274 square feet</p>
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<p>1274 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Since the building is square-shaped, dividing its area by 2 gives half of its area.</p>
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<p>Since the building is square-shaped, dividing its area by 2 gives half of its area.</p>
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<p>Dividing 2548 by 2 gives 1274.</p>
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<p>Dividing 2548 by 2 gives 1274.</p>
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<p>So, half of the building measures 1274 square feet.</p>
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<p>So, half of the building measures 1274 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 √2548 x 5.</p>
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<p>Calculate √2548 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 252.39</p>
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<p>Approximately 252.39</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 2548, which is approximately 50.48. Then multiply by 5: 50.48 x 5 = 252.39</p>
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<p>First, find the square root of 2548, which is approximately 50.48. Then multiply by 5: 50.48 x 5 = 252.39</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 (2500 + 48)?</p>
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<p>What will be the square root of (2500 + 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 50.48.</p>
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<p>The square root is approximately 50.48.</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, sum (2500 + 48), which equals 2548.</p>
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<p>To find the square root, sum (2500 + 48), which equals 2548.</p>
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<p>The square root of 2548 is approximately 50.48.</p>
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<p>The square root of 2548 is approximately 50.48.</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 √2548 units and the width ‘w’ is 30 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √2548 units and the width ‘w’ is 30 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 160.96 units.</p>
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<p>The perimeter of the rectangle is approximately 160.96 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width)</p>
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<p>Perimeter of a rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√2548 + 30)</p>
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<p>Perimeter = 2 × (√2548 + 30)</p>
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<p>= 2 × (50.48 + 30)</p>
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<p>= 2 × (50.48 + 30)</p>
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<p>= 2 × 80.48</p>
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<p>= 2 × 80.48</p>
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<p>= 160.96 units.</p>
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<p>= 160.96 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 2548</h2>
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<h2>FAQ on Square Root of 2548</h2>
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<h3>1.What is √2548 in its simplest form?</h3>
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<h3>1.What is √2548 in its simplest form?</h3>
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<p>The prime factorization of 2548 is 2^2 x 3^2 x 71, so the simplest form of √2548 is √(2^2 x 3^2 x 71).</p>
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<p>The prime factorization of 2548 is 2^2 x 3^2 x 71, so the simplest form of √2548 is √(2^2 x 3^2 x 71).</p>
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<h3>2.Mention the factors of 2548.</h3>
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<h3>2.Mention the factors of 2548.</h3>
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<p>The factors of 2548 include 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, and 2548.</p>
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<p>The factors of 2548 include 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, and 2548.</p>
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<h3>3.Calculate the square of 2548.</h3>
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<h3>3.Calculate the square of 2548.</h3>
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<p>The square of 2548 is found by multiplying 2548 by itself: 2548 x 2548 = 6497504.</p>
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<p>The square of 2548 is found by multiplying 2548 by itself: 2548 x 2548 = 6497504.</p>
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<h3>4.Is 2548 a prime number?</h3>
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<h3>4.Is 2548 a prime number?</h3>
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<p>2548 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>2548 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.2548 is divisible by?</h3>
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<h3>5.2548 is divisible by?</h3>
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<p>2548 is divisible by 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, and 2548.</p>
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<p>2548 is divisible by 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, and 2548.</p>
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<h2>Important Glossaries for the Square Root of 2548</h2>
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<h2>Important Glossaries for the Square Root of 2548</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 7^2 = 49, so √49 = 7. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 7^2 = 49, so √49 = 7. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. </li>
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<li><strong>Radical form:</strong>The expression of a number as a root, such as √x, is in radical form. </li>
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<li><strong>Radical form:</strong>The expression of a number as a root, such as √x, is in radical form. </li>
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<li><strong>Long division method:</strong>A method for finding square roots of numbers that involves dividing and averaging. </li>
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<li><strong>Long division method:</strong>A method for finding square roots of numbers that involves dividing and averaging. </li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer, such as 1, 4, 9, 16, etc.</li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer, such as 1, 4, 9, 16, etc.</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>