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Original
2026-01-01
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2026-02-28
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<p>244 Learners</p>
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<p>278 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 the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 728.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 728.</p>
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<h2>What is the Square Root of 728?</h2>
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<h2>What is the Square Root of 728?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 728 is not a<a>perfect square</a>. The square root of 728 can be expressed in both radical and exponential forms. In radical form, it is expressed as √728, whereas in<a>exponential form</a>it is (728)^(1/2). √728 ≈ 26.9737, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two<a>integers</a>(p/q, where q ≠ 0).</p>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 728 is not a<a>perfect square</a>. The square root of 728 can be expressed in both radical and exponential forms. In radical form, it is expressed as √728, whereas in<a>exponential form</a>it is (728)^(1/2). √728 ≈ 26.9737, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two<a>integers</a>(p/q, where q ≠ 0).</p>
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<h2>Finding the Square Root of 728</h2>
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<h2>Finding the Square Root of 728</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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, for non-perfect square numbers, methods like 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 728 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 728 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 728 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 728 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 728</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 728</p>
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<p>Breaking it down, we get 2 × 2 × 2 × 91 = 2^3 × 7 × 13</p>
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<p>Breaking it down, we get 2 × 2 × 2 × 91 = 2^3 × 7 × 13</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 728. The second step is to make pairs of those prime factors. Since 728 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √728 using prime factorization alone is impractical.</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 728. The second step is to make pairs of those prime factors. Since 728 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √728 using prime factorization alone is impractical.</p>
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<h2>Square Root of 728 by Long Division Method</h2>
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<h2>Square Root of 728 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<a>square root</a>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<a>square root</a>using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 728, we need to group it as 28 and 7.</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 728, we need to group it as 28 and 7.</p>
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<p><strong>Step 2</strong>: Now we need to find n whose square is<a>less than</a>or equal to the first group (7). We can say n is ‘2’ because 2 × 2 = 4, which is less than or equal to 7. Now the<a>quotient</a>is 2; after subtracting 4 from 7, the<a>remainder</a>is 3.</p>
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<p><strong>Step 2</strong>: Now we need to find n whose square is<a>less than</a>or equal to the first group (7). We can say n is ‘2’ because 2 × 2 = 4, which is less than or equal to 7. Now the<a>quotient</a>is 2; after subtracting 4 from 7, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now, bring down 28 to make it 328, which is the new<a>dividend</a>. Double the current quotient (2) to get 4, which becomes our new<a>divisor</a>(4_).</p>
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<p><strong>Step 3:</strong>Now, bring down 28 to make it 328, which is the new<a>dividend</a>. Double the current quotient (2) to get 4, which becomes our new<a>divisor</a>(4_).</p>
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<p><strong>Step 4:</strong>Find a digit to fill in the blank (4_) such that the product of this new number and the same digit is less than or equal to 328.</p>
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<p><strong>Step 4:</strong>Find a digit to fill in the blank (4_) such that the product of this new number and the same digit is less than or equal to 328.</p>
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<p><strong>Step 5:</strong>Continue this process until you achieve the desired precision. Using this method, you will find that √728 ≈ 26.97.</p>
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<p><strong>Step 5:</strong>Continue this process until you achieve the desired precision. Using this method, you will find that √728 ≈ 26.97.</p>
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<h2>Square Root of 728 by Approximation Method</h2>
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<h2>Square Root of 728 by Approximation Method</h2>
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<p>The approximation method is another method for finding the 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 728 using the approximation method.</p>
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<p>The approximation method is another method for finding the 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 728 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 728. The smallest perfect square less than 728 is 676 (26^2), and the largest perfect square<a>greater than</a>728 is 729 (27^2). Thus, √728 falls between 26 and 27.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 728. The smallest perfect square less than 728 is 676 (26^2), and the largest perfect square<a>greater than</a>728 is 729 (27^2). Thus, √728 falls between 26 and 27.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (728 - 676) / (729 - 676) = 52/53 ≈ 0.9811 Add this<a>decimal</a>to the smaller square root: 26 + 0.9811 = 26.9811 Therefore, the square root of 728 is approximately 26.9811.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (728 - 676) / (729 - 676) = 52/53 ≈ 0.9811 Add this<a>decimal</a>to the smaller square root: 26 + 0.9811 = 26.9811 Therefore, the square root of 728 is approximately 26.9811.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 728</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 728</h2>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Let us look at a few common mistakes in detail.</p>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Let us look at 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 √728?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √728?</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 728 square units.</p>
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<p>The area of the square is 728 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.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √728.</p>
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<p>The side length is given as √728.</p>
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<p>Area of the square = side^2 = √728 × √728 = 728.</p>
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<p>Area of the square = side^2 = √728 × √728 = 728.</p>
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<p>Therefore, the area of the square box is 728 square units.</p>
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<p>Therefore, the area of the square box is 728 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 728 square feet is built. If each of the sides is √728, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 728 square feet is built. If each of the sides is √728, 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>364 square feet</p>
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<p>364 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, as the building is square-shaped.</p>
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<p>We can divide the given area by 2, as the building is square-shaped.</p>
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<p>Dividing 728 by 2 gives us 364.</p>
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<p>Dividing 728 by 2 gives us 364.</p>
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<p>So, half of the building measures 364 square feet.</p>
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<p>So, half of the building measures 364 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 √728 × 5.</p>
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<p>Calculate √728 × 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>134.87</p>
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<p>134.87</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 728, which is approximately 26.97.</p>
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<p>The first step is to find the square root of 728, which is approximately 26.97.</p>
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<p>The second step is to multiply 26.97 by 5.</p>
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<p>The second step is to multiply 26.97 by 5.</p>
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<p>So, 26.97 × 5 ≈ 134.87.</p>
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<p>So, 26.97 × 5 ≈ 134.87.</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 (728 + 1)?</p>
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<p>What will be the square root of (728 + 1)?</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 27.</p>
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<p>The square root is 27.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (728 + 1). 728 + 1 = 729, and the square root of 729 is 27.</p>
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<p>To find the square root, we need to find the sum of (728 + 1). 728 + 1 = 729, and the square root of 729 is 27.</p>
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<p>Therefore, the square root of (728 + 1) is 27.</p>
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<p>Therefore, the square root of (728 + 1) is 27.</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 √728 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √728 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 129.94 units.</p>
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<p>The perimeter of the rectangle is 129.94 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√728 + 38) ≈ 2 × (26.97 + 38) ≈ 2 × 64.97 ≈ 129.94 units.</p>
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<p>Perimeter = 2 × (√728 + 38) ≈ 2 × (26.97 + 38) ≈ 2 × 64.97 ≈ 129.94 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 728</h2>
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<h2>FAQ on Square Root of 728</h2>
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<h3>1.What is √728 in its simplest form?</h3>
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<h3>1.What is √728 in its simplest form?</h3>
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<p>The prime factorization of 728 is 2 × 2 × 2 × 7 × 13, so the simplest form of √728 is √(2^3 × 7 × 13).</p>
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<p>The prime factorization of 728 is 2 × 2 × 2 × 7 × 13, so the simplest form of √728 is √(2^3 × 7 × 13).</p>
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<h3>2.Mention the factors of 728.</h3>
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<h3>2.Mention the factors of 728.</h3>
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<p>Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.</p>
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<p>Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.</p>
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<h3>3.Calculate the square of 728.</h3>
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<h3>3.Calculate the square of 728.</h3>
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<p>We get the square of 728 by multiplying the number by itself: 728 × 728 = 529,984.</p>
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<p>We get the square of 728 by multiplying the number by itself: 728 × 728 = 529,984.</p>
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<h3>4.Is 728 a prime number?</h3>
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<h3>4.Is 728 a prime number?</h3>
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<h3>5.728 is divisible by?</h3>
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<h3>5.728 is divisible by?</h3>
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<p>728 has many factors; these are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.</p>
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<p>728 has many factors; these are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.</p>
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<h2>Important Glossaries for the Square Root of 728</h2>
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<h2>Important Glossaries for the Square Root of 728</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root, √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root, √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Long division method:</strong>A mathematical procedure used to find the square root of numbers, especially non-perfect squares, by breaking down the calculation into simpler steps.</li>
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</ul><ul><li><strong>Long division method:</strong>A mathematical procedure used to find the square root of numbers, especially non-perfect squares, by breaking down the calculation into simpler steps.</li>
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</ul><ul><li><strong>Approximation method:</strong>A technique to estimate the value of a square root by using nearby perfect squares to find a closer value.</li>
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</ul><ul><li><strong>Approximation method:</strong>A technique to estimate the value of a square root by using nearby perfect squares to find a closer value.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors.</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>