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2026-01-01
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2026-02-28
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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 848.</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 848.</p>
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<h2>What is the Square Root of 848?</h2>
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<h2>What is the Square Root of 848?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 848 is not a<a>perfect square</a>. The square root of 848 is expressed in both radical and exponential forms. In the radical form, it is expressed as √848, whereas (848)^(1/2) in the<a>exponential form</a>. √848 ≈ 29.11, 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>. 848 is not a<a>perfect square</a>. The square root of 848 is expressed in both radical and exponential forms. In the radical form, it is expressed as √848, whereas (848)^(1/2) in the<a>exponential form</a>. √848 ≈ 29.11, 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 848</h2>
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<h2>Finding the Square Root of 848</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 848 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 848 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 848 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 848 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 848.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 848.</p>
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<p>Breaking it down, we get 2 x 2 x 2 x 2 x 53: 2^4 x 53^1</p>
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<p>Breaking it down, we get 2 x 2 x 2 x 2 x 53: 2^4 x 53^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 848. The second step is to make pairs of those prime factors. Since 848 is not a perfect square, the digits of the number can’t be grouped in pairs evenly. Therefore, calculating √848 using prime factorization is impossible.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 848. The second step is to make pairs of those prime factors. Since 848 is not a perfect square, the digits of the number can’t be grouped in pairs evenly. Therefore, calculating √848 using prime factorization is impossible.</p>
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<h2>Square Root of 848 by Long Division Method</h2>
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<h2>Square Root of 848 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 848, we need to group it as 48 and 8.</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 848, we need to group it as 48 and 8.</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 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</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 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 48, making the new<a>dividend</a>448. Add the old<a>divisor</a>, 2, to itself to get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 48, making the new<a>dividend</a>448. Add the old<a>divisor</a>, 2, to itself to get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Find n such that 4n x n ≤ 448. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 4:</strong>Find n such that 4n x n ≤ 448. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 5:</strong>Subtract 41 from 448, and the difference is 407. The quotient becomes 21.</p>
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<p><strong>Step 5:</strong>Subtract 41 from 448, and the difference is 407. The quotient becomes 21.</p>
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<p><strong>Step 6:</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 40700.</p>
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<p><strong>Step 6:</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 40700.</p>
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<p><strong>Step 7:</strong>Now find the new divisor, which is 211 because 211 x 1 is close to 40700.</p>
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<p><strong>Step 7:</strong>Now find the new divisor, which is 211 because 211 x 1 is close to 40700.</p>
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<p><strong>Step 8:</strong>Subtracting the result from 40700 gives the remainder. Repeat as necessary to obtain a more accurate quotient.</p>
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<p><strong>Step 8:</strong>Subtracting the result from 40700 gives the remainder. Repeat as necessary to obtain a more accurate quotient.</p>
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<p>So the square root of √848 ≈ 29.11.</p>
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<p>So the square root of √848 ≈ 29.11.</p>
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<h2>Square Root of 848 by Approximation Method</h2>
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<h2>Square Root of 848 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots, and 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 848 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots, and 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 848 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √848. The smallest perfect square less than 848 is 841 and the largest perfect square<a>greater than</a>848 is 900. √848 falls somewhere between 29 and 30.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √848. The smallest perfect square less than 848 is 841 and the largest perfect square<a>greater than</a>848 is 900. √848 falls somewhere between 29 and 30.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (848 - 841) / (900 - 841) ≈ 0.11.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (848 - 841) / (900 - 841) ≈ 0.11.</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 29 + 0.11 = 29.11, so the square root of 848 is approximately 29.11.</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 29 + 0.11 = 29.11, so the square root of 848 is approximately 29.11.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 848</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 848</h2>
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<p>Students do make mistakes while finding the square root, such as 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, such as 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 √848?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √848?</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 848 square units.</p>
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<p>The area of the square is approximately 848 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 √848.</p>
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<p>The side length is given as √848.</p>
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<p>Area of the square = side^2 = √848 x √848 = 848.</p>
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<p>Area of the square = side^2 = √848 x √848 = 848.</p>
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<p>Therefore, the area of the square box is 848 square units.</p>
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<p>Therefore, the area of the square box is 848 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 848 square feet is built; if each of the sides is √848, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 848 square feet is built; if each of the sides is √848, 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>424 square feet</p>
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<p>424 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 848 by 2 = we get 424.</p>
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<p>Dividing 848 by 2 = we get 424.</p>
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<p>So half of the building measures 424 square feet.</p>
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<p>So half of the building measures 424 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 √848 x 5.</p>
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<p>Calculate √848 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>145.55</p>
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<p>145.55</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 848, which is approximately 29.11.</p>
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<p>The first step is to find the square root of 848, which is approximately 29.11.</p>
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<p>The second step is to multiply 29.11 by 5.</p>
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<p>The second step is to multiply 29.11 by 5.</p>
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<p>So 29.11 x 5 = 145.55.</p>
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<p>So 29.11 x 5 = 145.55.</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 (144 + 704)?</p>
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<p>What will be the square root of (144 + 704)?</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 29.12.</p>
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<p>The square root is approximately 29.12.</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 (144 + 704). 144 + 704 = 848, and then √848 ≈ 29.12.</p>
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<p>To find the square root, we need to find the sum of (144 + 704). 144 + 704 = 848, and then √848 ≈ 29.12.</p>
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<p>Therefore, the square root of (144 + 704) is ±29.12.</p>
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<p>Therefore, the square root of (144 + 704) is ±29.12.</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 √848 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 √848 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 134.22 units.</p>
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<p>We find the perimeter of the rectangle as 134.22 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 × (√848 + 38) ≈ 2 × (29.11 + 38) ≈ 2 × 67.11 ≈ 134.22 units.</p>
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<p>Perimeter = 2 × (√848 + 38) ≈ 2 × (29.11 + 38) ≈ 2 × 67.11 ≈ 134.22 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 848</h2>
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<h2>FAQ on Square Root of 848</h2>
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<h3>1.What is √848 in its simplest form?</h3>
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<h3>1.What is √848 in its simplest form?</h3>
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<p>The prime factorization of 848 is 2 x 2 x 2 x 2 x 53, so the simplest form of √848 is √(2^4 x 53).</p>
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<p>The prime factorization of 848 is 2 x 2 x 2 x 2 x 53, so the simplest form of √848 is √(2^4 x 53).</p>
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<h3>2.Mention the factors of 848.</h3>
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<h3>2.Mention the factors of 848.</h3>
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<p>Factors of 848 are 1, 2, 4, 8, 16, 53, 106, 212, 424, and 848.</p>
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<p>Factors of 848 are 1, 2, 4, 8, 16, 53, 106, 212, 424, and 848.</p>
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<h3>3.Calculate the square of 848.</h3>
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<h3>3.Calculate the square of 848.</h3>
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<p>We get the square of 848 by multiplying the number by itself, that is 848 x 848 = 719104.</p>
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<p>We get the square of 848 by multiplying the number by itself, that is 848 x 848 = 719104.</p>
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<h3>4.Is 848 a prime number?</h3>
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<h3>4.Is 848 a prime number?</h3>
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<h3>5.848 is divisible by?</h3>
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<h3>5.848 is divisible by?</h3>
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<p>848 has many factors; those are 1, 2, 4, 8, 16, 53, 106, 212, 424, and 848.</p>
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<p>848 has many factors; those are 1, 2, 4, 8, 16, 53, 106, 212, 424, and 848.</p>
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<h2>Important Glossaries for the Square Root of 848</h2>
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<h2>Important Glossaries for the Square Root of 848</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; 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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<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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<li><strong>Prime factorization:</strong>Breaking down a number into its basic building blocks (prime numbers) is called prime factorization. For example, the prime factorization of 848 is 2^4 x 53. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic building blocks (prime numbers) is called prime factorization. For example, the prime factorization of 848 is 2^4 x 53. </li>
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<li><strong>Long division method:</strong>A technique for finding the square root of a non-perfect square by dividing the number into groups and calculating step-by-step for an accurate approximation.</li>
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<li><strong>Long division method:</strong>A technique for finding the square root of a non-perfect square by dividing the number into groups and calculating step-by-step for an accurate approximation.</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>