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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 37.5</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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 37.5</p>
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<h2>What is the Square Root of 37.5?</h2>
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<h2>What is the Square Root of 37.5?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 37.5 is not a<a>perfect square</a>. The square root of 37.5 is expressed in both radical and exponential forms. In the radical form, it is expressed as √37.5, whereas (37.5)^(1/2) in the<a>exponential form</a>. √37.5 ≈ 6.12372, 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>. 37.5 is not a<a>perfect square</a>. The square root of 37.5 is expressed in both radical and exponential forms. In the radical form, it is expressed as √37.5, whereas (37.5)^(1/2) in the<a>exponential form</a>. √37.5 ≈ 6.12372, 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 37.5</h2>
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<h2>Finding the Square Root of 37.5</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>and approximation methods 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>and approximation methods 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 37.5 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 37.5 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 37.5 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 37.5 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Convert 37.5 into a<a>fraction</a>: 375/10.</p>
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<p><strong>Step 1:</strong>Convert 37.5 into a<a>fraction</a>: 375/10.</p>
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<p><strong>Step 2:</strong>Find the prime factors of the<a>numerator</a>375, which are 3 × 5 × 5 × 5.</p>
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<p><strong>Step 2:</strong>Find the prime factors of the<a>numerator</a>375, which are 3 × 5 × 5 × 5.</p>
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<p><strong>Step 3:</strong>Find the prime factors of the<a>denominator</a>10, which are 2 × 5.</p>
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<p><strong>Step 3:</strong>Find the prime factors of the<a>denominator</a>10, which are 2 × 5.</p>
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<p><strong>Step 4:</strong>Therefore, √37.5 = √(375/10) = √(3 × 5 × 5 × 5/2 × 5).</p>
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<p><strong>Step 4:</strong>Therefore, √37.5 = √(375/10) = √(3 × 5 × 5 × 5/2 × 5).</p>
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<p><strong>Step 5:</strong>Simplify the<a>expression</a>: √(3 × 5 × 5 × 5/2 × 5) = √(3 × 5 × 5/2).</p>
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<p><strong>Step 5:</strong>Simplify the<a>expression</a>: √(3 × 5 × 5 × 5/2 × 5) = √(3 × 5 × 5/2).</p>
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<p>Since 37.5 is not a perfect square, calculating using prime factorization will still require approximation.</p>
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<p>Since 37.5 is not a perfect square, calculating using prime factorization will still require approximation.</p>
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<h2>Square Root of 37.5 by Long Division Method</h2>
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<h2>Square Root of 37.5 by Long Division Method</h2>
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<p>The<a>long 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<a>long 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 37.5, consider it similar to 3750 and group it as 37 and 50.</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 37.5, consider it similar to 3750 and group it as 37 and 50.</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 37. We can say n as ‘6’ because 6 × 6 = 36, which is lesser than or equal to 37. Now the<a>quotient</a>is 6 and the<a>remainder</a>is 1.</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 37. We can say n as ‘6’ because 6 × 6 = 36, which is lesser than or equal to 37. Now the<a>quotient</a>is 6 and the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Bring down 50, making the new<a>dividend</a>150.</p>
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<p><strong>Step 3:</strong>Bring down 50, making the new<a>dividend</a>150.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>is 2 × 6 = 12. Find n such that 12n × n ≤ 150.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>is 2 × 6 = 12. Find n such that 12n × n ≤ 150.</p>
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<p><strong>Step 5:</strong>Consider n as 1, now 121 × 1 = 121.</p>
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<p><strong>Step 5:</strong>Consider n as 1, now 121 × 1 = 121.</p>
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<p><strong>Step 6:</strong>Subtract 121 from 150, the remainder is 29, and the quotient is 61.</p>
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<p><strong>Step 6:</strong>Subtract 121 from 150, the remainder is 29, and the quotient is 61.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point and two zeros to the dividend, making it 2900.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point and two zeros to the dividend, making it 2900.</p>
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<p><strong>Step 8:</strong>Find the new divisor which is 122 because 1220 × 2 = 2440.</p>
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<p><strong>Step 8:</strong>Find the new divisor which is 122 because 1220 × 2 = 2440.</p>
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<p><strong>Step 9:</strong>Subtract 2440 from 2900, resulting in 460. Step 10: The quotient is 6.12.</p>
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<p><strong>Step 9:</strong>Subtract 2440 from 2900, resulting in 460. Step 10: The quotient is 6.12.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until you achieve the desired decimal places.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until you achieve the desired decimal places.</p>
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<p>So the square root of √37.5 ≈ 6.12372.</p>
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<p>So the square root of √37.5 ≈ 6.12372.</p>
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<h2>Square Root of 37.5 by Approximation Method</h2>
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<h2>Square Root of 37.5 by Approximation Method</h2>
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<p>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 37.5 using the approximation method.</p>
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<p>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 37.5 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √37.5. The smallest perfect square less than 37.5 is 36 and the largest perfect square<a>greater than</a>37.5 is 49. √37.5 falls between 6 and 7.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √37.5. The smallest perfect square less than 37.5 is 36 and the largest perfect square<a>greater than</a>37.5 is 49. √37.5 falls between 6 and 7.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p>(Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>
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<p>(Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>
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<p>Using the formula: (37.5 - 36) / (49 - 36) = 1.5 / 13 ≈ 0.1154</p>
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<p>Using the formula: (37.5 - 36) / (49 - 36) = 1.5 / 13 ≈ 0.1154</p>
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<p><strong> Step 3:</strong>Add this<a>decimal</a>to the smaller perfect square root: 6 + 0.1154 ≈ 6.1154.</p>
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<p><strong> Step 3:</strong>Add this<a>decimal</a>to the smaller perfect square root: 6 + 0.1154 ≈ 6.1154.</p>
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<p>So, the approximate square root of 37.5 is 6.1154.</p>
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<p>So, the approximate square root of 37.5 is 6.1154.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 37.5</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 37.5</h2>
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<p>Students make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. 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 √37.5?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √37.5?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 37.5 square units.</p>
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<p>The area of the square is approximately 37.5 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 √37.5.</p>
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<p>The side length is given as √37.5.</p>
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<p>Area of the square = side^2 = √37.5 × √37.5 ≈ 6.12372 × 6.12372 = 37.5.</p>
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<p>Area of the square = side^2 = √37.5 × √37.5 ≈ 6.12372 × 6.12372 = 37.5.</p>
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<p>Therefore, the area of the square box is 37.5 square units.</p>
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<p>Therefore, the area of the square box is 37.5 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 37.5 square meters is planned; if each of the sides is √37.5, what will be the square meters of half of the garden?</p>
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<p>A square-shaped garden measuring 37.5 square meters is planned; if each of the sides is √37.5, what will be the square meters 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>18.75 square meters</p>
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<p>18.75 square meters</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 37.5 by 2 gives us 18.75.</p>
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<p>Dividing 37.5 by 2 gives us 18.75.</p>
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<p>So half of the garden measures 18.75 square meters.</p>
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<p>So half of the garden measures 18.75 square meters.</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 √37.5 × 5.</p>
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<p>Calculate √37.5 × 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 30.6186</p>
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<p>Approximately 30.6186</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 37.5, which is approximately 6.12372.</p>
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<p>The first step is to find the square root of 37.5, which is approximately 6.12372.</p>
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<p>The second step is to multiply 6.12372 with 5. So 6.12372 × 5 ≈ 30.6186.</p>
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<p>The second step is to multiply 6.12372 with 5. So 6.12372 × 5 ≈ 30.6186.</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 (25 + 12.5)?</p>
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<p>What will be the square root of (25 + 12.5)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is 6.</p>
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<p>The square root is 6.</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 (25 + 12.5). 25 + 12.5 = 37.5, and then √37.5 ≈ 6.12372.</p>
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<p>To find the square root, we need to find the sum of (25 + 12.5). 25 + 12.5 = 37.5, and then √37.5 ≈ 6.12372.</p>
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<p>Therefore, the square root of (25 + 12.5) is approximately 6.12372.</p>
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<p>Therefore, the square root of (25 + 12.5) is approximately 6.12372.</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 √37.5 units and the width ‘w’ is 10 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √37.5 units and the width ‘w’ is 10 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 32.24744 units.</p>
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<p>The perimeter of the rectangle is approximately 32.24744 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 × (√37.5 + 10) ≈ 2 × (6.12372 + 10) ≈ 2 × 16.12372 ≈ 32.24744 units.</p>
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<p>Perimeter = 2 × (√37.5 + 10) ≈ 2 × (6.12372 + 10) ≈ 2 × 16.12372 ≈ 32.24744 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 37.5</h2>
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<h2>FAQ on Square Root of 37.5</h2>
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<h3>1.What is √37.5 in its simplest form?</h3>
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<h3>1.What is √37.5 in its simplest form?</h3>
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<p>The simplest form of √37.5 is obtained by converting it into a fraction and simplifying: √(375/10) = √(3 × 5 × 5/2).</p>
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<p>The simplest form of √37.5 is obtained by converting it into a fraction and simplifying: √(375/10) = √(3 × 5 × 5/2).</p>
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<h3>2.Mention the factors of 37.5.</h3>
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<h3>2.Mention the factors of 37.5.</h3>
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<p>Factors of 37.5 are 1, 2.5, 5, 7.5, 12.5, 15, and 37.5.</p>
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<p>Factors of 37.5 are 1, 2.5, 5, 7.5, 12.5, 15, and 37.5.</p>
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<h3>3.Calculate the square of 37.5.</h3>
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<h3>3.Calculate the square of 37.5.</h3>
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<p>We get the square of 37.5 by multiplying the number by itself: 37.5 × 37.5 = 1406.25.</p>
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<p>We get the square of 37.5 by multiplying the number by itself: 37.5 × 37.5 = 1406.25.</p>
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<h3>4.Is 37.5 a prime number?</h3>
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<h3>4.Is 37.5 a prime number?</h3>
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<p>37.5 is not a<a>prime number</a>, as it is not an integer, and prime numbers are defined only for integers.</p>
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<p>37.5 is not a<a>prime number</a>, as it is not an integer, and prime numbers are defined only for integers.</p>
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<h3>5.37.5 is divisible by?</h3>
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<h3>5.37.5 is divisible by?</h3>
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<p>37.5 is divisible by 1, 2.5, 5, 7.5, 12.5, 15, and 37.5.</p>
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<p>37.5 is divisible by 1, 2.5, 5, 7.5, 12.5, 15, and 37.5.</p>
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<h2>Important Glossaries for the Square Root of 37.5</h2>
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<h2>Important Glossaries for the Square Root of 37.5</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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<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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<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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<li><strong>Principal square root:</strong>A number has both positive and negative square roots, but it is usually the positive square root that is used due to its practical applications. This is known as the principal square root. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots, but it is usually the positive square root that is used due to its practical applications. This is known as the principal square root. </li>
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<li><strong>Approximation method:</strong>A method used to estimate the value of a square root by finding the nearest perfect squares and using them to calculate a closer value. </li>
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<li><strong>Approximation method:</strong>A method used to estimate the value of a square root by finding the nearest perfect squares and using them to calculate a closer value. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of a number by dividing it into groups and performing a series of divisions and subtractions to achieve the desired precision.</li>
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<li><strong>Long division method:</strong>A method used to find the square root of a number by dividing it into groups and performing a series of divisions and subtractions to achieve the desired precision.</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>