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2026-01-01
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2026-02-28
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<p>196 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, finance, etc. Here, we will discuss the square root of 709.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, finance, etc. Here, we will discuss the square root of 709.</p>
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<h2>What is the Square Root of 709?</h2>
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<h2>What is the Square Root of 709?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 709 is not a<a>perfect square</a>. The square root of 709 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √709, whereas in exponential form it is expressed as (709)^(1/2). √709 ≈ 26.62705, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 709 is not a<a>perfect square</a>. The square root of 709 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √709, whereas in exponential form it is expressed as (709)^(1/2). √709 ≈ 26.62705, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 709</h2>
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<h2>Finding the Square Root of 709</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where long-<a>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 709 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 709 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 709 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 709 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 709 709 is a<a>prime number</a>, so it cannot be broken down further. The prime factorization of 709 is simply 709^1.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 709 709 is a<a>prime number</a>, so it cannot be broken down further. The prime factorization of 709 is simply 709^1.</p>
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<p><strong>Step 2:</strong>Since 709 is not a perfect square, calculating √709 using prime factorization is not feasible. We will use other methods such as the<a>long division</a>method or approximation method.</p>
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<p><strong>Step 2:</strong>Since 709 is not a perfect square, calculating √709 using prime factorization is not feasible. We will use other methods such as the<a>long division</a>method or approximation method.</p>
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<h2>Square Root of 709 by Long Division Method</h2>
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<h2>Square Root of 709 by Long Division Method</h2>
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<p>The long division 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 division 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 709, we group it as 09 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 709, we group it as 09 and 7.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 7. We can say n as ‘2’ because 2^2 = 4, which is<a>less than</a>7. The<a>quotient</a>is 2, and after subtracting 4 from 7, we get a<a>remainder</a>of 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 7. We can say n as ‘2’ because 2^2 = 4, which is<a>less than</a>7. The<a>quotient</a>is 2, and after subtracting 4 from 7, we get a<a>remainder</a>of 3.</p>
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<p><strong>Step 3:</strong>Bring down 09, making the new<a>dividend</a>309. Double the quotient (2) and write it as 4_, where _ is the next digit of the<a>divisor</a>. Step 4: Find a digit n such that 4n × n ≤ 309. Using trial, we find n = 6, as 46 × 6 = 276.</p>
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<p><strong>Step 3:</strong>Bring down 09, making the new<a>dividend</a>309. Double the quotient (2) and write it as 4_, where _ is the next digit of the<a>divisor</a>. Step 4: Find a digit n such that 4n × n ≤ 309. Using trial, we find n = 6, as 46 × 6 = 276.</p>
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<p><strong>Step 5:</strong>Subtract 276 from 309, leaving a remainder of 33. The quotient so far is 26.</p>
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<p><strong>Step 5:</strong>Subtract 276 from 309, leaving a remainder of 33. The quotient so far is 26.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point and bring down pairs of zeroes. The next dividend is 3300.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point and bring down pairs of zeroes. The next dividend is 3300.</p>
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<p><strong>Step 7:</strong>Find a new divisor by doubling the current quotient (26) and adding the next digit. Repeat the process to find the next digits of the quotient until the desired precision is achieved.</p>
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<p><strong>Step 7:</strong>Find a new divisor by doubling the current quotient (26) and adding the next digit. Repeat the process to find the next digits of the quotient until the desired precision is achieved.</p>
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<p><strong>Step 8:</strong>Continue until you get two numbers after the decimal point. The approximate square root of √709 is 26.63.</p>
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<p><strong>Step 8:</strong>Continue until you get two numbers after the decimal point. The approximate square root of √709 is 26.63.</p>
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<h2>Square Root of 709 by Approximation Method</h2>
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<h2>Square Root of 709 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 709 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 709 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares surrounding 709. The smallest perfect square less than 709 is 676 (26^2), and the largest perfect square<a>greater than</a>709 is 729 (27^2). √709 falls between 26 and 27.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares surrounding 709. The smallest perfect square less than 709 is 676 (26^2), and the largest perfect square<a>greater than</a>709 is 729 (27^2). √709 falls between 26 and 27.</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). (709 - 676) / (729 - 676) = 33 / 53 ≈ 0.6226 Using the formula, we identified the decimal point of our square root. Add this value to the smaller integer square root: 26 + 0.6226 ≈ 26.63. Therefore, the square root of 709 is approximately 26.63.</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). (709 - 676) / (729 - 676) = 33 / 53 ≈ 0.6226 Using the formula, we identified the decimal point of our square root. Add this value to the smaller integer square root: 26 + 0.6226 ≈ 26.63. Therefore, the square root of 709 is approximately 26.63.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 709</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 709</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few of those mistakes in detail.</p>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few of those 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 √709?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √709?</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 709 square units.</p>
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<p>The area of the square is approximately 709 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>The side length is given as √709.</p>
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<p>The side length is given as √709.</p>
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<p>Area of the square = (√709) × (√709) = 709.</p>
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<p>Area of the square = (√709) × (√709) = 709.</p>
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<p>Therefore, the area of the square box is 709 square units.</p>
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<p>Therefore, the area of the square box is 709 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 garden measuring 709 square feet is built; if each of the sides is √709, what will be the square feet of half of the garden?</p>
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<p>A square-shaped garden measuring 709 square feet is built; if each of the sides is √709, what will be the square feet of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>354.5 square feet</p>
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<p>354.5 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the garden is square-shaped.</p>
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<p>We can just divide the given area by 2 as the garden is square-shaped.</p>
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<p>Dividing 709 by 2 gives us 354.5.</p>
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<p>Dividing 709 by 2 gives us 354.5.</p>
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<p>So, half of the garden measures 354.5 square feet.</p>
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<p>So, half of the garden measures 354.5 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 √709 × 5.</p>
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<p>Calculate √709 × 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 133.13525</p>
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<p>Approximately 133.13525</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 709, which is approximately 26.62705.</p>
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<p>The first step is to find the square root of 709, which is approximately 26.62705.</p>
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<p>The second step is to multiply 26.62705 by 5.</p>
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<p>The second step is to multiply 26.62705 by 5.</p>
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<p>So, 26.62705 × 5 ≈ 133.13525.</p>
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<p>So, 26.62705 × 5 ≈ 133.13525.</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 (700 + 9)?</p>
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<p>What will be the square root of (700 + 9)?</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 26.63.</p>
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<p>The square root is approximately 26.63.</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 calculate the sum of 700 + 9, which is 709.</p>
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<p>To find the square root, we calculate the sum of 700 + 9, which is 709.</p>
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<p>The square root of 709 is approximately 26.63.</p>
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<p>The square root of 709 is approximately 26.63.</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 √709 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 √709 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 129.2541 units.</p>
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<p>The perimeter of the rectangle is approximately 129.2541 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 × (√709 + 38) = 2 × (26.62705 + 38) = 2 × 64.62705 = 129.2541 units.</p>
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<p>Perimeter = 2 × (√709 + 38) = 2 × (26.62705 + 38) = 2 × 64.62705 = 129.2541 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 709</h2>
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<h2>FAQ on Square Root of 709</h2>
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<h3>1.What is √709 in its simplest form?</h3>
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<h3>1.What is √709 in its simplest form?</h3>
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<p>709 is a prime number, so its simplest radical form is √709.</p>
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<p>709 is a prime number, so its simplest radical form is √709.</p>
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<h3>2.Is 709 a prime number?</h3>
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<h3>2.Is 709 a prime number?</h3>
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<p>Yes, 709 is a prime number as it has only two factors, 1 and 709.</p>
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<p>Yes, 709 is a prime number as it has only two factors, 1 and 709.</p>
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<h3>3.Calculate the square of 709.</h3>
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<h3>3.Calculate the square of 709.</h3>
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<p>We get the square of 709 by multiplying the number by itself, which is 709 × 709 = 502681.</p>
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<p>We get the square of 709 by multiplying the number by itself, which is 709 × 709 = 502681.</p>
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<h3>4.709 is divisible by?</h3>
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<h3>4.709 is divisible by?</h3>
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<p>709 is a prime number and is only divisible by 1 and 709.</p>
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<p>709 is a prime number and is only divisible by 1 and 709.</p>
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<h3>5.What are some uses of square roots?</h3>
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<h3>5.What are some uses of square roots?</h3>
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<p>Square roots are used in various fields like engineering, physics, finance, and<a>statistics</a>for calculations involving<a>quadratic equations</a>, area computations, and<a>data</a>analysis.</p>
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<p>Square roots are used in various fields like engineering, physics, finance, and<a>statistics</a>for calculations involving<a>quadratic equations</a>, area computations, and<a>data</a>analysis.</p>
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<h2>Important Glossaries for the Square Root of 709</h2>
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<h2>Important Glossaries for the Square Root of 709</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 square root of 16 is √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 square root of 16 is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. For example, √709 is irrational.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. For example, √709 is irrational.</li>
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</ul><ul><li><strong>Prime number:</strong>A prime number has only two distinct positive divisors: 1 and itself. For example, 709 is a prime number.</li>
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</ul><ul><li><strong>Prime number:</strong>A prime number has only two distinct positive divisors: 1 and itself. For example, 709 is a prime number.</li>
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</ul><ul><li><strong>Radical:</strong>A symbol (√) used to denote the root of a number. For example, √709 represents the square root of 709.</li>
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</ul><ul><li><strong>Radical:</strong>A symbol (√) used to denote the root of a number. For example, √709 represents the square root of 709.</li>
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</ul><ul><li><strong>Approximation:</strong>The process of finding a value that is close to the actual value. For example, √709 is approximately 26.63.</li>
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</ul><ul><li><strong>Approximation:</strong>The process of finding a value that is close to the actual value. For example, √709 is approximately 26.63.</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>