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2026-01-01
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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 vehicle design, finance, etc. Here, we will discuss the square root of 306.25</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 vehicle design, finance, etc. Here, we will discuss the square root of 306.25</p>
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<h2>What is the Square Root of 306.25?</h2>
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<h2>What is the Square Root of 306.25?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 306.25 is not a<a>perfect square</a>. The square root of 306.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √306.25, whereas (306.25)^(1/2) in exponential form. √306.25 = 17.5, which is a<a>rational number</a>because it can 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<a>of</a>the square of the<a>number</a>. 306.25 is not a<a>perfect square</a>. The square root of 306.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √306.25, whereas (306.25)^(1/2) in exponential form. √306.25 = 17.5, which is a<a>rational number</a>because it can 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 306.25</h2>
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<h2>Finding the Square Root of 306.25</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 typically used for non-perfect square numbers where long-<a>division</a>method and approximation method are generally applied. 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 typically used for non-perfect square numbers where long-<a>division</a>method and approximation method are generally applied. 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 306.25 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 306.25 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 306.25 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 306.25 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Converting 306.25 to a<a>fraction</a>for easier factoring gives us 30625/100.</p>
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<p><strong>Step 1:</strong>Converting 306.25 to a<a>fraction</a>for easier factoring gives us 30625/100.</p>
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<p><strong>Step 2:</strong>Finding the prime factors of 30625, we have 5^2 × 1225. Further factoring 1225, we get 5^2 × 7^2. So, 30625 = 5^4 × 7^2.</p>
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<p><strong>Step 2:</strong>Finding the prime factors of 30625, we have 5^2 × 1225. Further factoring 1225, we get 5^2 × 7^2. So, 30625 = 5^4 × 7^2.</p>
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<p><strong>Step 3:</strong>The prime factorization of 306.25 in<a>decimal</a>form involves taking the<a>square root</a>of each prime factor pair. √(5^4 × 7^2) = 5^2 × 7 = 25 × 7 = 175. Since we are working with a fraction (30625/100), we need to take the square root of the<a>denominator</a>as well: √100 = 10.</p>
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<p><strong>Step 3:</strong>The prime factorization of 306.25 in<a>decimal</a>form involves taking the<a>square root</a>of each prime factor pair. √(5^4 × 7^2) = 5^2 × 7 = 25 × 7 = 175. Since we are working with a fraction (30625/100), we need to take the square root of the<a>denominator</a>as well: √100 = 10.</p>
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<p>The final result is 175/10 = 17.5.</p>
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<p>The final result is 175/10 = 17.5.</p>
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<h2>Square Root of 306.25 by Long Division Method</h2>
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<h2>Square Root of 306.25 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, pair the digits of 306.25 from right to left as 06|25|00.</p>
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<p><strong>Step 1:</strong>To begin with, pair the digits of 306.25 from right to left as 06|25|00.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to the first pair (06). That number is 2. Place 2 above the line.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to the first pair (06). That number is 2. Place 2 above the line.</p>
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<p><strong>Step 3:</strong>Subtract 4 (2^2) from 6, bringing down the next pair to get 225.</p>
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<p><strong>Step 3:</strong>Subtract 4 (2^2) from 6, bringing down the next pair to get 225.</p>
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<p><strong>Step 4:</strong>The<a>divisor</a>is 4 now, and placing 7 next to it gives 47. Find a digit n such that 47n × n ≤ 225.</p>
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<p><strong>Step 4:</strong>The<a>divisor</a>is 4 now, and placing 7 next to it gives 47. Find a digit n such that 47n × n ≤ 225.</p>
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<p><strong>Step 5:</strong>n = 5 as 475 × 5 = 225. Subtract to get 0, and bring down the next pair, 00.</p>
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<p><strong>Step 5:</strong>n = 5 as 475 × 5 = 225. Subtract to get 0, and bring down the next pair, 00.</p>
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<p><strong>Step 6:</strong>The next divisor is 50, placing 0 next to it gives 500.</p>
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<p><strong>Step 6:</strong>The next divisor is 50, placing 0 next to it gives 500.</p>
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<p>Since we have no<a>remainder</a>, the square root is 17.5.</p>
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<p>Since we have no<a>remainder</a>, the square root is 17.5.</p>
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<h2>Square Root of 306.25 by Approximation Method</h2>
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<h2>Square Root of 306.25 by Approximation Method</h2>
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<p>The approximation method is another method for finding the square roots; it is an easy way to find the square root of a given number. Now let us learn how to find the square root of 306.25 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 way to find the square root of a given number. Now let us learn how to find the square root of 306.25 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares surrounding 306.25. The smallest perfect square is 289 (17^2), and the largest perfect square is 324 (18^2).</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares surrounding 306.25. The smallest perfect square is 289 (17^2), and the largest perfect square is 324 (18^2).</p>
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<p><strong>Step 2:</strong>Since 306.25 is closer to 289, we approximate its square root as between 17 and 18.</p>
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<p><strong>Step 2:</strong>Since 306.25 is closer to 289, we approximate its square root as between 17 and 18.</p>
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<p><strong>Step 3:</strong>Calculate the decimal point using interpolation. The<a>formula</a>is: (Given number - smallest perfect square) / (Difference between perfect squares) (306.25 - 289) / (324 - 289) = 17.5 The final approximation is 17.5, so the square root of 306.25 is 17.5.</p>
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<p><strong>Step 3:</strong>Calculate the decimal point using interpolation. The<a>formula</a>is: (Given number - smallest perfect square) / (Difference between perfect squares) (306.25 - 289) / (324 - 289) = 17.5 The final approximation is 17.5, so the square root of 306.25 is 17.5.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 306.25</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 306.25</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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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 √200?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √200?</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 200 square units.</p>
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<p>The area of the square is 200 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 √200.</p>
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<p>The side length is given as √200.</p>
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<p>Area of the square = side^2 = √200 x √200 = 200.</p>
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<p>Area of the square = side^2 = √200 x √200 = 200.</p>
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<p>Therefore, the area of the square box is 200 square units.</p>
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<p>Therefore, the area of the square box is 200 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 306.25 square feet is built; if each of the sides is √306.25, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 306.25 square feet is built; if each of the sides is √306.25, 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>153.125 square feet</p>
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<p>153.125 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 building is square-shaped.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 306.25 by 2 = we get 153.125.</p>
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<p>Dividing 306.25 by 2 = we get 153.125.</p>
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<p>So half of the building measures 153.125 square feet.</p>
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<p>So half of the building measures 153.125 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 √306.25 x 5.</p>
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<p>Calculate √306.25 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>87.5</p>
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<p>87.5</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 306.25, which is 17.5.</p>
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<p>The first step is to find the square root of 306.25, which is 17.5.</p>
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<p>The second step is to multiply 17.5 by 5.</p>
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<p>The second step is to multiply 17.5 by 5.</p>
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<p>So, 17.5 x 5 = 87.5.</p>
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<p>So, 17.5 x 5 = 87.5.</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 (200 + 6.25)?</p>
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<p>What will be the square root of (200 + 6.25)?</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 14.5.</p>
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<p>The square root is 14.5.</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 (200 + 6.25). 200 + 6.25 = 206.25, and then √206.25 = 14.5.</p>
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<p>To find the square root, we need to find the sum of (200 + 6.25). 200 + 6.25 = 206.25, and then √206.25 = 14.5.</p>
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<p>Therefore, the square root of (200 + 6.25) is ±14.5.</p>
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<p>Therefore, the square root of (200 + 6.25) is ±14.5.</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 √200 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 √200 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>We find the perimeter of the rectangle as 99.48 units.</p>
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<p>We find the perimeter of the rectangle as 99.48 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 × (√200 + 38) = 2 × (14.14 + 38) = 2 × 52.14 = 104.28 units.</p>
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<p>Perimeter = 2 × (√200 + 38) = 2 × (14.14 + 38) = 2 × 52.14 = 104.28 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 306.25</h2>
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<h2>FAQ on Square Root of 306.25</h2>
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<h3>1.What is √306.25 in its simplest form?</h3>
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<h3>1.What is √306.25 in its simplest form?</h3>
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<p>The prime factorization of 306.25 is 5^2 × 7, so the simplest form of √306.25 = 5 × √7.</p>
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<p>The prime factorization of 306.25 is 5^2 × 7, so the simplest form of √306.25 = 5 × √7.</p>
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<h3>2.Mention the factors of 306.25.</h3>
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<h3>2.Mention the factors of 306.25.</h3>
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<p>Factors of 306.25 in fraction form are 1, 5, 25, 5^2 × 7, and 306.25.</p>
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<p>Factors of 306.25 in fraction form are 1, 5, 25, 5^2 × 7, and 306.25.</p>
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<h3>3.Calculate the square of 306.25.</h3>
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<h3>3.Calculate the square of 306.25.</h3>
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<p>We get the square of 306.25 by multiplying the number by itself, that is, 306.25 × 306.25 = 93751.5625.</p>
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<p>We get the square of 306.25 by multiplying the number by itself, that is, 306.25 × 306.25 = 93751.5625.</p>
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<h3>4.Is 306.25 a prime number?</h3>
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<h3>4.Is 306.25 a prime number?</h3>
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<p>306.25 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>306.25 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.306.25 is divisible by?</h3>
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<h3>5.306.25 is divisible by?</h3>
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<p>306.25 is divisible by 5 and 25, among others.</p>
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<p>306.25 is divisible by 5 and 25, among others.</p>
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<h2>Important Glossaries for the Square Root of 306.25</h2>
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<h2>Important Glossaries for the Square Root of 306.25</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Interpolation:</strong>Interpolation is a method of estimating unknown values that fall between known values.</li>
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</ul><ul><li><strong>Interpolation:</strong>Interpolation is a method of estimating unknown values that fall between known values.</li>
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</ul><ul><li><strong>Factorization:</strong>Factorization is the process of breaking down numbers into their constituent prime factors.</li>
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</ul><ul><li><strong>Factorization:</strong>Factorization is the process of breaking down numbers into their constituent 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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<p>▶</p>
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<p>▶</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>