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Original
2026-01-01
Modified
2026-02-28
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<p>207 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. Square roots are used in various fields, including engineering and finance. Here, we will discuss the square root of 652.</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. Square roots are used in various fields, including engineering and finance. Here, we will discuss the square root of 652.</p>
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<h2>What is the Square Root of 652?</h2>
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<h2>What is the Square Root of 652?</h2>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 652 is not a<a>perfect square</a>. The square root of 652 can be expressed in both radical form and<a>exponential form</a>. In radical form, it is expressed as √652, and in exponential form as \(652^{1/2}\). The value of √652 is approximately 25.529, which is an<a>irrational number</a>as it cannot be expressed as a<a>fraction</a>of two integers.</p>
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<p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 652 is not a<a>perfect square</a>. The square root of 652 can be expressed in both radical form and<a>exponential form</a>. In radical form, it is expressed as √652, and in exponential form as \(652^{1/2}\). The value of √652 is approximately 25.529, which is an<a>irrational number</a>as it cannot be expressed as a<a>fraction</a>of two integers.</p>
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<h2>Finding the Square Root of 652</h2>
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<h2>Finding the Square Root of 652</h2>
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<p>The<a>prime factorization</a>method is typically used for perfect square numbers. However, for non-perfect squares, methods like<a>long division</a>and approximation are used. Let's explore these methods:</p>
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<p>The<a>prime factorization</a>method is typically used for perfect square numbers. However, for non-perfect squares, methods like<a>long division</a>and approximation are used. Let's 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 652 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 652 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 break down 652 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 break down 652 into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 652 Breaking it down, we get 2 x 2 x 163: (2^2 times 163^1)</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 652 Breaking it down, we get 2 x 2 x 163: (2^2 times 163^1)</p>
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<p><strong>Step 2:</strong>Since 652 is not a perfect square, we cannot group all the prime factors into pairs.</p>
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<p><strong>Step 2:</strong>Since 652 is not a perfect square, we cannot group all the prime factors into pairs.</p>
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<p>Therefore, calculating √652 using prime factorization alone is not feasible.</p>
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<p>Therefore, calculating √652 using prime factorization alone is not feasible.</p>
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<h2>Square Root of 652 by Long Division Method</h2>
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<h2>Square Root of 652 by Long Division Method</h2>
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<p>The long<a>division</a>method is useful for finding the<a>square root</a>of non-perfect squares. Here is how to use this method step-by-step:</p>
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<p>The long<a>division</a>method is useful for finding the<a>square root</a>of non-perfect squares. Here is how to use this method step-by-step:</p>
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<p><strong>Step 1:</strong>Group the digits of 652 from right to left as '52' and '6'.</p>
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<p><strong>Step 1:</strong>Group the digits of 652 from right to left as '52' and '6'.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 6. This number is 2, since (2^2 = 4). Subtract 4 from 6, leaving a<a>remainder</a>of 2.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 6. This number is 2, since (2^2 = 4). Subtract 4 from 6, leaving a<a>remainder</a>of 2.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, 52, to get the new<a>dividend</a>, 252. Double the<a>divisor</a>from step 2 (2), giving us 4, and append a digit to form a new divisor.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, 52, to get the new<a>dividend</a>, 252. Double the<a>divisor</a>from step 2 (2), giving us 4, and append a digit to form a new divisor.</p>
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<p><strong>Step 4:</strong>Determine the largest digit, n, so that 4n x n ≤ 252. Here, n = 5, since 45 x 5 = 225.</p>
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<p><strong>Step 4:</strong>Determine the largest digit, n, so that 4n x n ≤ 252. Here, n = 5, since 45 x 5 = 225.</p>
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<p><strong>Step 5:</strong>Subtract 225 from 252, resulting in a remainder of 27. Bring down two zeros to form the new dividend, 2700.</p>
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<p><strong>Step 5:</strong>Subtract 225 from 252, resulting in a remainder of 27. Bring down two zeros to form the new dividend, 2700.</p>
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<p><strong>Step 6:</strong>Repeat the process until the desired precision is achieved. Our<a>quotient</a>so far is approximately 25.52.</p>
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<p><strong>Step 6:</strong>Repeat the process until the desired precision is achieved. Our<a>quotient</a>so far is approximately 25.52.</p>
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<h2>Square Root of 652 by Approximation Method</h2>
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<h2>Square Root of 652 by Approximation Method</h2>
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<p>The approximation method provides a quick way to estimate square roots. Here's how to find √652 using approximation:</p>
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<p>The approximation method provides a quick way to estimate square roots. Here's how to find √652 using approximation:</p>
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<p><strong>Step 1:</strong>Identify perfect squares nearest to 652. The closest perfect squares are 625 (25²) and 676 (26²). Therefore, √652 is between 25 and 26.</p>
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<p><strong>Step 1:</strong>Identify perfect squares nearest to 652. The closest perfect squares are 625 (25²) and 676 (26²). Therefore, √652 is between 25 and 26.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: ((text{Given number} - text{Lower perfect square}) / (text{Higher perfect square} - text{Lower perfect square})). Calculating, we get: ((652 - 625) / (676 - 625) = 27 / 51 approx 0.529).</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: ((text{Given number} - text{Lower perfect square}) / (text{Higher perfect square} - text{Lower perfect square})). Calculating, we get: ((652 - 625) / (676 - 625) = 27 / 51 approx 0.529).</p>
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<p><strong>Step 3:</strong>Add this<a>decimal</a>to the lower square root: 25 + 0.529 = 25.529.</p>
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<p><strong>Step 3:</strong>Add this<a>decimal</a>to the lower square root: 25 + 0.529 = 25.529.</p>
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<p>Hence, the approximate value of √652 is 25.529.</p>
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<p>Hence, the approximate value of √652 is 25.529.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 652</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 652</h2>
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<p>Students often make errors while finding square roots, such as neglecting the negative square root or misapplying methods. Let's explore common mistakes in more detail.</p>
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<p>Students often make errors while finding square roots, such as neglecting the negative square root or misapplying methods. Let's explore common mistakes in more 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 √652?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √652?</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 box is 652 square units.</p>
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<p>The area of the square box is 652 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 given by side².</p>
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<p>The area of a square is given by side².</p>
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<p>The side length is √652, so the area is (√652)² = 652.</p>
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<p>The side length is √652, so the area is (√652)² = 652.</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 plot measuring 652 square feet is constructed. If each side is √652 feet, what is the area of half the plot?</p>
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<p>A square-shaped plot measuring 652 square feet is constructed. If each side is √652 feet, what is the area of half the plot?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>326 square feet</p>
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<p>326 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Since the plot is square-shaped, dividing the total area by 2 gives the area of half the plot.</p>
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<p>Since the plot is square-shaped, dividing the total area by 2 gives the area of half the plot.</p>
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<p>652 / 2 = 326</p>
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<p>652 / 2 = 326</p>
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<p>So, half of the plot measures 326 square feet.</p>
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<p>So, half of the plot measures 326 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 √652 x 5.</p>
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<p>Calculate √652 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>127.645</p>
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<p>127.645</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 652, approximately 25.529, then multiply by 5:</p>
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<p>First, find the square root of 652, approximately 25.529, then multiply by 5:</p>
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<p>25.529 x 5 = 127.645.</p>
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<p>25.529 x 5 = 127.645.</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 is the square root of (652 + 48)?</p>
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<p>What is the square root of (652 + 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>26</p>
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<p>26</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the sum of 652 + 48 = 700.</p>
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<p>First, find the sum of 652 + 48 = 700.</p>
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<p>The square root of 700 is approximately 26.457, but if rounded to the nearest whole number, it is 26.</p>
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<p>The square root of 700 is approximately 26.457, but if rounded to the nearest whole number, it is 26.</p>
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<p>Therefore, the square root of 700 is approximately ±26.</p>
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<p>Therefore, the square root of 700 is approximately ±26.</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 a rectangle if its length ‘l’ is √652 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √652 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>The perimeter of the rectangle is approximately 127.058 units.</p>
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<p>The perimeter of the rectangle is approximately 127.058 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 × (√652 + 38)</p>
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<p>Perimeter = 2 × (√652 + 38)</p>
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<p>= 2 × (25.529 + 38)</p>
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<p>= 2 × (25.529 + 38)</p>
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<p>= 2 × 63.529</p>
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<p>= 2 × 63.529</p>
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<p>= 127.058 units.</p>
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<p>= 127.058 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 652</h2>
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<h2>FAQ on Square Root of 652</h2>
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<h3>1.What is √652 in its simplest form?</h3>
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<h3>1.What is √652 in its simplest form?</h3>
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<p>The prime factorization of 652 is 2 x 2 x 163, so the simplest form of √652 is √(2² × 163).</p>
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<p>The prime factorization of 652 is 2 x 2 x 163, so the simplest form of √652 is √(2² × 163).</p>
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<h3>2.Mention the factors of 652.</h3>
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<h3>2.Mention the factors of 652.</h3>
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<p>Factors of 652 are 1, 2, 4, 163, 326, and 652.</p>
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<p>Factors of 652 are 1, 2, 4, 163, 326, and 652.</p>
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<h3>3.Calculate the square of 652.</h3>
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<h3>3.Calculate the square of 652.</h3>
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<p>The square of 652 is obtained by multiplying the number by itself: 652 x 652 = 425,104.</p>
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<p>The square of 652 is obtained by multiplying the number by itself: 652 x 652 = 425,104.</p>
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<h3>4.Is 652 a prime number?</h3>
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<h3>4.Is 652 a prime number?</h3>
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<p>No, 652 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>No, 652 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.652 is divisible by?</h3>
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<h3>5.652 is divisible by?</h3>
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<p>652 is divisible by 1, 2, 4, 163, 326, and 652.</p>
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<p>652 is divisible by 1, 2, 4, 163, 326, and 652.</p>
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<h2>Important Glossaries for the Square Root of 652</h2>
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<h2>Important Glossaries for the Square Root of 652</h2>
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<ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. Example: \(5^2 = 25\), and the square root of 25 is √25 = 5. </li>
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<ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. Example: \(5^2 = 25\), and the square root of 25 is √25 = 5. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. </li>
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<li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 25 is a perfect square because it is (5^2). </li>
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<li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 25 is a perfect square because it is (5^2). </li>
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<li><strong>Long division method:</strong>A technique used to find the square root of numbers that are not perfect squares. </li>
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<li><strong>Long division method:</strong>A technique used to find the square root of numbers that are not perfect squares. </li>
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<li><strong>Approximation:</strong>A method to estimate the value of a mathematical expression, often using nearby or simpler values.</li>
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<li><strong>Approximation:</strong>A method to estimate the value of a mathematical expression, often using nearby or simpler values.</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>