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2026-01-01
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2026-02-28
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<p>204 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 taking the square root. The square root concept is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 872.</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 taking the square root. The square root concept is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 872.</p>
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<h2>What is the Square Root of 872?</h2>
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<h2>What is the Square Root of 872?</h2>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 872 is not a<a>perfect square</a>. The square root of 872 can be expressed in both radical and exponential forms. In radical form, it is expressed as √872, whereas in<a>exponential form</a>, it is expressed as (872)^(1/2). Calculating the approximate value, √872 ≈ 29.5305, which is an<a>irrational number</a>because it cannot be expressed in the form 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 operation of squaring a<a>number</a>. 872 is not a<a>perfect square</a>. The square root of 872 can be expressed in both radical and exponential forms. In radical form, it is expressed as √872, whereas in<a>exponential form</a>, it is expressed as (872)^(1/2). Calculating the approximate value, √872 ≈ 29.5305, which is an<a>irrational number</a>because it cannot be expressed in the form p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 872</h2>
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<h2>Finding the Square Root of 872</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 like 872, methods such as the long-<a>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 like 872, methods such as the long-<a>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 872 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 872 by Prime Factorization Method</h2>
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<p>Prime factorization involves expressing a number as a<a>product</a>of prime<a>factors</a>. However, for non-perfect squares like 872, we cannot proceed with pairing prime factors. Let us look at how 872 is broken down into its prime factors.</p>
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<p>Prime factorization involves expressing a number as a<a>product</a>of prime<a>factors</a>. However, for non-perfect squares like 872, we cannot proceed with pairing prime factors. Let us look at how 872 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 872</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 872</p>
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<p>Breaking it down, we get 2 x 2 x 2 x 109: 2^3 x 109</p>
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<p>Breaking it down, we get 2 x 2 x 2 x 109: 2^3 x 109</p>
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<p><strong>Step 2:</strong>Since 872 is not a perfect square, the digits of the number cannot be grouped in pairs. Thus, calculating √872 using prime factorization directly is not feasible.</p>
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<p><strong>Step 2:</strong>Since 872 is not a perfect square, the digits of the number cannot be grouped in pairs. Thus, calculating √872 using prime factorization directly is not feasible.</p>
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<h2>Square Root of 872 by Long Division Method</h2>
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<h2>Square Root of 872 by Long Division Method</h2>
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<p>The<a>long division</a>method is useful for finding the<a>square root</a>of non-perfect square numbers. Here's how you can find the square root using this method:</p>
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<p>The<a>long division</a>method is useful for finding the<a>square root</a>of non-perfect square numbers. Here's how you can find the square root using this method:</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left in pairs. For 872, group as 87 and 2.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left in pairs. For 872, group as 87 and 2.</p>
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<p><strong>Step 2:</strong>Find a number whose square is ≤ 87. The number is 9 because 9^2 = 81 ≤ 87. The<a>quotient</a>becomes 9, and the<a>remainder</a>is 6 (87 - 81).</p>
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<p><strong>Step 2:</strong>Find a number whose square is ≤ 87. The number is 9 because 9^2 = 81 ≤ 87. The<a>quotient</a>becomes 9, and the<a>remainder</a>is 6 (87 - 81).</p>
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<p><strong>Step 3:</strong>Bring down the next pair, 2, making the new<a>dividend</a>62.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, 2, making the new<a>dividend</a>62.</p>
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<p><strong>Step 4:</strong>Double the quotient (9) to get 18, which will be part of the new<a>divisor</a>.</p>
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<p><strong>Step 4:</strong>Double the quotient (9) to get 18, which will be part of the new<a>divisor</a>.</p>
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<p><strong>Step 5:</strong>Determine a digit, d, such that (180 + d) × d ≤ 620. The digit is 3, making the divisor 183.</p>
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<p><strong>Step 5:</strong>Determine a digit, d, such that (180 + d) × d ≤ 620. The digit is 3, making the divisor 183.</p>
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<p><strong>Step 6:</strong>Multiply and subtract: 183 × 3 = 549, and 620 - 549 = 71.</p>
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<p><strong>Step 6:</strong>Multiply and subtract: 183 × 3 = 549, and 620 - 549 = 71.</p>
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<p><strong>Step 7:</strong>Add a<a>decimal</a>point and bring down pairs of zeros to continue the process until you reach the desired precision.</p>
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<p><strong>Step 7:</strong>Add a<a>decimal</a>point and bring down pairs of zeros to continue the process until you reach the desired precision.</p>
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<p>The square root of 872 using the long division method is approximately 29.5305.</p>
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<p>The square root of 872 using the long division method is approximately 29.5305.</p>
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<h2>Square Root of 872 by Approximation Method</h2>
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<h2>Square Root of 872 by Approximation Method</h2>
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<p>The approximation method is another way to find the square root of a number. Here's how to find the square root of 872 using this method:</p>
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<p>The approximation method is another way to find the square root of a number. Here's how to find the square root of 872 using this method:</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 872. The smallest perfect square is 841 (29^2) and the largest is 900 (30^2). √872 is between 29 and 30.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 872. The smallest perfect square is 841 (29^2) and the largest is 900 (30^2). √872 is between 29 and 30.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (872 - 841) / (900 - 841) = 31 / 59 ≈ 0.525</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (872 - 841) / (900 - 841) = 31 / 59 ≈ 0.525</p>
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<p><strong>Step 3:</strong>Add this to the smaller square root: 29 + 0.525 = 29.525</p>
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<p><strong>Step 3:</strong>Add this to the smaller square root: 29 + 0.525 = 29.525</p>
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<p>So, the square root of 872 is approximately 29.525.</p>
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<p>So, the square root of 872 is approximately 29.525.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 872</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 872</h2>
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<p>Students make mistakes such as forgetting about negative square roots and skipping steps in the long division method. Let us address a few common mistakes in detail.</p>
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<p>Students make mistakes such as forgetting about negative square roots and skipping steps in the long division method. Let us address a few 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 √872?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √872?</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 872 square units.</p>
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<p>The area of the square is approximately 872 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 = side^2.</p>
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<p>The area of a square = side^2.</p>
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<p>The side length is √872.</p>
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<p>The side length is √872.</p>
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<p>Area = (√872) × (√872) = 872</p>
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<p>Area = (√872) × (√872) = 872</p>
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<p>Therefore, the area of the square box is 872 square units.</p>
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<p>Therefore, the area of the square box is 872 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 872 square feet is built; if each of the sides is √872, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 872 square feet is built; if each of the sides is √872, 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>436 square feet</p>
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<p>436 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can divide the given area by 2 since the building is square-shaped.</p>
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<p>We can divide the given area by 2 since the building is square-shaped.</p>
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<p>Dividing 872 by 2 = 436</p>
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<p>Dividing 872 by 2 = 436</p>
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<p>So, half of the building measures 436 square feet.</p>
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<p>So, half of the building measures 436 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 √872 × 5.</p>
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<p>Calculate √872 × 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 147.6525</p>
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<p>Approximately 147.6525</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 872, which is approximately 29.5305.</p>
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<p>First, find the square root of 872, which is approximately 29.5305.</p>
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<p>Then multiply by 5. 29.5305 × 5 ≈ 147.6525</p>
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<p>Then multiply by 5. 29.5305 × 5 ≈ 147.6525</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 (800 + 72)?</p>
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<p>What will be the square root of (800 + 72)?</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 30</p>
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<p>The square root is 30</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, first calculate the sum: 800 + 72 = 872, and then calculate the square root. √872 ≈ 29.5305, but since the question specifies rounding, we use 30 for practical purposes.</p>
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<p>To find the square root, first calculate the sum: 800 + 72 = 872, and then calculate the square root. √872 ≈ 29.5305, but since the question specifies rounding, we use 30 for practical purposes.</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 √872 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 √872 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>The perimeter of the rectangle is approximately 159.061 units.</p>
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<p>The perimeter of the rectangle is approximately 159.061 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 × (√872 + 50) ≈ 2 × (29.5305 + 50) = 2 × 79.5305 = 159.061 units.</p>
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<p>Perimeter = 2 × (√872 + 50) ≈ 2 × (29.5305 + 50) = 2 × 79.5305 = 159.061 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 872</h2>
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<h2>FAQ on Square Root of 872</h2>
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<h3>1.What is √872 in its simplest form?</h3>
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<h3>1.What is √872 in its simplest form?</h3>
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<p>The prime factorization of 872 is 2 x 2 x 2 x 109, so the simplest form of √872 is √(2^3 x 109).</p>
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<p>The prime factorization of 872 is 2 x 2 x 2 x 109, so the simplest form of √872 is √(2^3 x 109).</p>
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<h3>2.Mention the factors of 872.</h3>
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<h3>2.Mention the factors of 872.</h3>
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<p>Factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872.</p>
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<p>Factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872.</p>
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<h3>3.Calculate the square of 872.</h3>
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<h3>3.Calculate the square of 872.</h3>
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<p>To find the square of 872, multiply the number by itself: 872 x 872 = 760,384.</p>
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<p>To find the square of 872, multiply the number by itself: 872 x 872 = 760,384.</p>
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<h3>4.Is 872 a prime number?</h3>
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<h3>4.Is 872 a prime number?</h3>
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<p>872 is not a<a>prime number</a>because it has more than two factors.</p>
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<p>872 is not a<a>prime number</a>because it has more than two factors.</p>
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<h3>5.872 is divisible by?</h3>
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<h3>5.872 is divisible by?</h3>
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<p>872 is divisible by 1, 2, 4, 8, 109, 218, 436, and 872.</p>
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<p>872 is divisible by 1, 2, 4, 8, 109, 218, 436, and 872.</p>
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<h2>Important Glossaries for the Square Root of 872</h2>
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<h2>Important Glossaries for the Square Root of 872</h2>
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<ul><li><strong>Square root:</strong>The square root is the inverse of squaring a 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>The square root is the inverse of squaring a 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 where both numerator and denominator are integers, with the denominator not being zero. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction where both numerator and denominator are integers, with the denominator not being zero. </li>
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<li><strong>Long division method:</strong>A technique used to find the square root of non-perfect-square numbers through systematic division. </li>
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<li><strong>Long division method:</strong>A technique used to find the square root of non-perfect-square numbers through systematic division. </li>
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<li><strong>Radical expression:</strong>An expression that includes a root symbol, such as a square root or cube root. </li>
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<li><strong>Radical expression:</strong>An expression that includes a root symbol, such as a square root or cube root. </li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 16 is a perfect square because 4^2 = 16.</li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 16 is a perfect square because 4^2 = 16.</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>