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2026-01-01
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2026-02-28
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<p>220 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 750.</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 750.</p>
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<h2>What is the Square Root of 750?</h2>
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<h2>What is the Square Root of 750?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 750 is not a<a>perfect square</a>. The square root of 750 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √750, whereas (750)^(1/2) in the exponential form. √750 ≈ 27.38613, 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<a>of</a>the square of the<a>number</a>. 750 is not a<a>perfect square</a>. The square root of 750 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √750, whereas (750)^(1/2) in the exponential form. √750 ≈ 27.38613, 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 750</h2>
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<h2>Finding the Square Root of 750</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 750 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 750 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 750 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 750 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 750 Breaking it down, we get 2 × 3 × 5 × 5 × 5: 2^1 × 3^1 × 5^3</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 750 Breaking it down, we get 2 × 3 × 5 × 5 × 5: 2^1 × 3^1 × 5^3</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 750. The second step is to make pairs of those prime factors. Since 750 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 750. The second step is to make pairs of those prime factors. Since 750 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 750 using prime factorization is impossible.</p>
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<p>Therefore, calculating 750 using prime factorization is impossible.</p>
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<h2>Square Root of 750 by Long Division Method</h2>
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<h2>Square Root of 750 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 750, we need to group it as 50 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 750, we need to group it as 50 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 is ‘2’ because 2 × 2 = 4 which is lesser 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 7. We can say n is ‘2’ because 2 × 2 = 4 which is lesser 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 let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 350. Let us consider n as 7, now 4 × 7 × 7 = 343.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 350. Let us consider n as 7, now 4 × 7 × 7 = 343.</p>
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<p><strong>Step 6:</strong>Subtract 343 from 350, the difference is 7, and the quotient is 27.</p>
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<p><strong>Step 6:</strong>Subtract 343 from 350, the difference is 7, and the quotient is 27.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 700.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 700.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 273 because 273 × 3 = 819.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 273 because 273 × 3 = 819.</p>
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<p><strong>Step 9:</strong>Subtracting 819 from 700 we get the result of -119.</p>
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<p><strong>Step 9:</strong>Subtracting 819 from 700 we get the result of -119.</p>
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<p><strong>Step 10:</strong>Now the quotient is approximately 27.3.</p>
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<p><strong>Step 10:</strong>Now the quotient is approximately 27.3.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √750 is approximately 27.39.</p>
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<p>So the square root of √750 is approximately 27.39.</p>
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<h2>Square Root of 750 by Approximation Method</h2>
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<h2>Square Root of 750 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 750 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 750 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √750.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √750.</p>
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<p>The smallest perfect square of 750 is 729 and the largest perfect square of 750 is 784. √750 falls somewhere between 27 and 28.</p>
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<p>The smallest perfect square of 750 is 729 and the largest perfect square of 750 is 784. √750 falls somewhere between 27 and 28.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (750 - 729) ÷ (784 - 729) = 21 ÷ 55 ≈ 0.3818.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (750 - 729) ÷ (784 - 729) = 21 ÷ 55 ≈ 0.3818.</p>
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<p>Using the formula we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 27 + 0.3818 ≈ 27.38, so the square root of 750 is approximately 27.38.</p>
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<p>Using the formula we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number which is 27 + 0.3818 ≈ 27.38, so the square root of 750 is approximately 27.38.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 750</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 750</h2>
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<p>Students do make mistakes while finding the square root, likewise 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, likewise 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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<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 √750?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √750?</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 750 square units.</p>
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<p>The area of the square is approximately 750 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 √750.</p>
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<p>The side length is given as √750.</p>
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<p>Area of the square = side^2 = √750 × √750 = 750.</p>
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<p>Area of the square = side^2 = √750 × √750 = 750.</p>
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<p>Therefore, the area of the square box is approximately 750 square units.</p>
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<p>Therefore, the area of the square box is approximately 750 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 750 square feet is built; if each of the sides is √750, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 750 square feet is built; if each of the sides is √750, 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>375 square feet</p>
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<p>375 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 750 by 2 = we get 375.</p>
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<p>Dividing 750 by 2 = we get 375.</p>
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<p>So half of the building measures 375 square feet.</p>
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<p>So half of the building measures 375 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 √750 × 5.</p>
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<p>Calculate √750 × 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 136.93</p>
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<p>Approximately 136.93</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 750 which is approximately 27.39, the second step is to multiply 27.39 with 5. So 27.39 × 5 ≈ 136.95.</p>
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<p>The first step is to find the square root of 750 which is approximately 27.39, the second step is to multiply 27.39 with 5. So 27.39 × 5 ≈ 136.95.</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 (750 + 30)?</p>
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<p>What will be the square root of (750 + 30)?</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 28.28</p>
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<p>The square root is approximately 28.28</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 (750 + 30). 750 + 30 = 780, and then √780 ≈ 28.28.</p>
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<p>To find the square root, we need to find the sum of (750 + 30). 750 + 30 = 780, and then √780 ≈ 28.28.</p>
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<p>Therefore, the square root of (750 + 30) is approximately ±28.28.</p>
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<p>Therefore, the square root of (750 + 30) is approximately ±28.28.</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 √750 units and the width ‘w’ is 30 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √750 units and the width ‘w’ is 30 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 approximately 114.78 units.</p>
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<p>We find the perimeter of the rectangle as approximately 114.78 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 × (√750 + 30) = 2 × (27.39 + 30) = 2 × 57.39 ≈ 114.78 units.</p>
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<p>Perimeter = 2 × (√750 + 30) = 2 × (27.39 + 30) = 2 × 57.39 ≈ 114.78 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 750</h2>
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<h2>FAQ on Square Root of 750</h2>
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<h3>1.What is √750 in its simplest form?</h3>
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<h3>1.What is √750 in its simplest form?</h3>
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<p>The prime factorization of 750 is 2 × 3 × 5 × 5 × 5, so the simplest form of √750 = √(2 × 3 × 5 × 5 × 5).</p>
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<p>The prime factorization of 750 is 2 × 3 × 5 × 5 × 5, so the simplest form of √750 = √(2 × 3 × 5 × 5 × 5).</p>
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<h3>2.Mention the factors of 750.</h3>
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<h3>2.Mention the factors of 750.</h3>
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<p>Factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.</p>
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<p>Factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.</p>
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<h3>3.Calculate the square of 750.</h3>
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<h3>3.Calculate the square of 750.</h3>
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<p>We get the square of 750 by multiplying the number by itself, that is 750 × 750 = 562,500.</p>
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<p>We get the square of 750 by multiplying the number by itself, that is 750 × 750 = 562,500.</p>
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<h3>4.Is 750 a prime number?</h3>
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<h3>4.Is 750 a prime number?</h3>
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<h3>5.750 is divisible by?</h3>
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<h3>5.750 is divisible by?</h3>
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<p>750 has many factors; those are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.</p>
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<p>750 has many factors; those are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.</p>
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<h2>Important Glossaries for the Square Root of 750</h2>
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<h2>Important Glossaries for the Square Root of 750</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>Irrational number:</strong>An irrational number is a number that cannot 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>Irrational number:</strong>An irrational number is a number that cannot 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 a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a 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 a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.</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>