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2026-01-01
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2026-02-28
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<p>266 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3456.</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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3456.</p>
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<h2>What is the Square Root of 3456?</h2>
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<h2>What is the Square Root of 3456?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 3456 is not a<a>perfect square</a>. The square root of 3456 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √3456, whereas in exponential form it is (3456)^(1/2). √3456 ≈ 58.78775, 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>. 3456 is not a<a>perfect square</a>. The square root of 3456 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √3456, whereas in exponential form it is (3456)^(1/2). √3456 ≈ 58.78775, 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 3456</h2>
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<h2>Finding the Square Root of 3456</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 the 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 the 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><h3>Square Root of 3456 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 3456 by Prime Factorization Method</h3>
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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 3456 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 3456 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 3456. Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3: 2^6 ×<a>3^4</a></p>
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<p><strong>Step 1:</strong>Finding the prime factors of 3456. Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3: 2^6 ×<a>3^4</a></p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 3456. The second step is to make pairs of those prime factors. Since 3456 is not a perfect square, the digits of the number can’t be grouped into pairs evenly. Therefore, calculating √3456 using prime factorization alone is not straightforward.</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 3456. The second step is to make pairs of those prime factors. Since 3456 is not a perfect square, the digits of the number can’t be grouped into pairs evenly. Therefore, calculating √3456 using prime factorization alone is not straightforward.</p>
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<h3>Square Root of 3456 by Long Division Method</h3>
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<h3>Square Root of 3456 by Long Division Method</h3>
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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 3456, we need to group it as 56 and 34.</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 3456, we need to group it as 56 and 34.</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 34. The closest such number is 5, since 5 × 5 = 25. Now the<a>quotient</a>is 5, and after subtracting 25 from 34, the<a>remainder</a>is 9.</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 34. The closest such number is 5, since 5 × 5 = 25. Now the<a>quotient</a>is 5, and after subtracting 25 from 34, the<a>remainder</a>is 9.</p>
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<p><strong>Step 3:</strong>Bring down 56, making the new<a>dividend</a>956. Add the old<a>divisor</a>with the quotient 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 56, making the new<a>dividend</a>956. Add the old<a>divisor</a>with the quotient 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n × n ≤ 956. Considering n as 9, 10 × 9 × 9 = 810. Step 5: Subtract 810 from 956; the difference is 146, and the quotient so far is 59.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n × n ≤ 956. Considering n as 9, 10 × 9 × 9 = 810. Step 5: Subtract 810 from 956; the difference is 146, and the quotient so far is 59.</p>
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<p><strong>Step 6:</strong>Since the dividend is more significant than the divisor, add a decimal point and bring down two zeros, making the new dividend 14600.</p>
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<p><strong>Step 6:</strong>Since the dividend is more significant than the divisor, add a decimal point and bring down two zeros, making the new dividend 14600.</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 118 because 1189 × 9 = 10701.</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 118 because 1189 × 9 = 10701.</p>
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<p><strong>Step 8:</strong>Subtracting 10701 from 14600, we get the result 3899.</p>
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<p><strong>Step 8:</strong>Subtracting 10701 from 14600, we get the result 3899.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we reach the desired precision. So the square root of √3456 ≈ 58.78775</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we reach the desired precision. So the square root of √3456 ≈ 58.78775</p>
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<h3>Square Root of 3456 by Approximation Method</h3>
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<h3>Square Root of 3456 by Approximation Method</h3>
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<p>The approximation method is another way to find 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 3456 using the approximation method.</p>
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<p>The approximation method is another way to find 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 3456 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √3456. The smallest perfect square less than 3456 is 3364, and the largest perfect square<a>greater than</a>3456 is 3481. √3456 falls somewhere between 58 and 59.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √3456. The smallest perfect square less than 3456 is 3364, and the largest perfect square<a>greater than</a>3456 is 3481. √3456 falls somewhere between 58 and 59.</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: (3456 - 3364) / (3481 - 3364) = 92 / 117 ≈ 0.78632 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the integer part we found initially to the decimal number, which is 58 + 0.78632 ≈ 58.78775.</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: (3456 - 3364) / (3481 - 3364) = 92 / 117 ≈ 0.78632 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the integer part we found initially to the decimal number, which is 58 + 0.78632 ≈ 58.78775.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3456</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3456</h2>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes in detail.</p>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √3456?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √3456?</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 3456 square units.</p>
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<p>The area of the square is approximately 3456 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 = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √3456.</p>
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<p>The side length is given as √3456.</p>
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<p>Area of the square = side² = √3456 × √3456 = 3456.</p>
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<p>Area of the square = side² = √3456 × √3456 = 3456.</p>
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<p>Therefore, the area of the square box is approximately 3456 square units.</p>
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<p>Therefore, the area of the square box is approximately 3456 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 3456 square feet is built; if each of the sides is √3456, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 3456 square feet is built; if each of the sides is √3456, 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>1728 square feet</p>
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<p>1728 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find half of the building's area, divide the given area by 2.</p>
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<p>To find half of the building's area, divide the given area by 2.</p>
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<p>Dividing 3456 by 2, we get 1728.</p>
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<p>Dividing 3456 by 2, we get 1728.</p>
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<p>So half of the building measures 1728 square feet.</p>
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<p>So half of the building measures 1728 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 √3456 × 5.</p>
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<p>Calculate √3456 × 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>293.93875</p>
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<p>293.93875</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 3456, which is approximately 58.78775.</p>
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<p>The first step is to find the square root of 3456, which is approximately 58.78775.</p>
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<p>The second step is to multiply this by 5.</p>
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<p>The second step is to multiply this by 5.</p>
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<p>So 58.78775 × 5 ≈ 293.93875.</p>
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<p>So 58.78775 × 5 ≈ 293.93875.</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 (3450 + 6)?</p>
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<p>What will be the square root of (3450 + 6)?</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 59.</p>
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<p>The square root is 59.</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, first find the sum of (3450 + 6). 3450 + 6 = 3456, and then √3456 ≈ 58.78775 ≈ 59 (rounded to the nearest whole number). Therefore, the square root of (3450 + 6) is approximately ±59.</p>
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<p>To find the square root, first find the sum of (3450 + 6). 3450 + 6 = 3456, and then √3456 ≈ 58.78775 ≈ 59 (rounded to the nearest whole number). Therefore, the square root of (3450 + 6) is approximately ±59.</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 √3456 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 √3456 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 193.5755 units.</p>
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<p>The perimeter of the rectangle is approximately 193.5755 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). Perimeter = 2 × (√3456 + 38) = 2 × (58.78775 + 38) ≈ 2 × 96.78775 ≈ 193.5755 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3456 + 38) = 2 × (58.78775 + 38) ≈ 2 × 96.78775 ≈ 193.5755 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 3456</h2>
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<h2>FAQ on Square Root of 3456</h2>
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<h3>1.What is √3456 in its simplest form?</h3>
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<h3>1.What is √3456 in its simplest form?</h3>
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<p>The prime factorization of 3456 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3, so the simplest form of √3456 is √(2^6 × 3^4).</p>
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<p>The prime factorization of 3456 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3, so the simplest form of √3456 is √(2^6 × 3^4).</p>
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<h3>2.Mention the factors of 3456.</h3>
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<h3>2.Mention the factors of 3456.</h3>
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<p>Factors of 3456 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1152, 1728, and 3456.</p>
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<p>Factors of 3456 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1152, 1728, and 3456.</p>
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<h3>3.Calculate the square of 3456.</h3>
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<h3>3.Calculate the square of 3456.</h3>
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<p>We get the square of 3456 by multiplying the number by itself: 3456 × 3456 = 11,943,936.</p>
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<p>We get the square of 3456 by multiplying the number by itself: 3456 × 3456 = 11,943,936.</p>
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<h3>4.Is 3456 a prime number?</h3>
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<h3>4.Is 3456 a prime number?</h3>
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<p>3456 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>3456 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.3456 is divisible by?</h3>
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<h3>5.3456 is divisible by?</h3>
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<p>3456 is divisible by several numbers, including 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1152, 1728, and 3456.</p>
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<p>3456 is divisible by several numbers, including 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1152, 1728, and 3456.</p>
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<h2>Important Glossaries for the Square Root of 3456</h2>
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<h2>Important Glossaries for the Square Root of 3456</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number 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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</ul><ul><li><strong>Irrational number:</strong>An irrational number 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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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the principal square root is the positive one, which is commonly used.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the principal square root is the positive one, which is commonly used.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.</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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<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>