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2026-01-01
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2026-02-28
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<p>223 Learners</p>
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<p>248 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 itself, 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 3360.</p>
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<p>If a number is multiplied by itself, 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 3360.</p>
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<h2>What is the Square Root of 3360?</h2>
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<h2>What is the Square Root of 3360?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 3360 is not a<a>perfect square</a>. The square root of 3360 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √3360, whereas in exponential form it is expressed as (3360)^(1/2). √3360 ≈ 57.9332, 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 a<a>number</a>. 3360 is not a<a>perfect square</a>. The square root of 3360 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √3360, whereas in exponential form it is expressed as (3360)^(1/2). √3360 ≈ 57.9332, 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 3360</h2>
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<h2>Finding the Square Root of 3360</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><h3>Square Root of 3360 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 3360 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 3360 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 3360 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 3360 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7: 2^4 x 3 x 5 x 7^2</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 3360 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7: 2^4 x 3 x 5 x 7^2</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 3360. The next step is to make pairs of those prime factors. Since 3360 is not a perfect square, the digits of the number can’t be grouped into pairs completely. Therefore, calculating √3360 using prime factorization directly is not feasible.</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 3360. The next step is to make pairs of those prime factors. Since 3360 is not a perfect square, the digits of the number can’t be grouped into pairs completely. Therefore, calculating √3360 using prime factorization directly is not feasible.</p>
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<h3>Square Root of 3360 by Long Division Method</h3>
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<h3>Square Root of 3360 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, group the numbers from right to left. In the case of 3360, we need to group it as 33 and 60.</p>
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<p><strong>Step 1:</strong>To begin with, group the numbers from right to left. In the case of 3360, we need to group it as 33 and 60.</p>
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<p><strong>Step 2:</strong>Now find n whose square is<a>less than</a>or equal to 33. We can say n is '5' because 5 x 5 = 25, which is less than 33. The<a>quotient</a>is 5 after subtracting 25 from 33, the<a>remainder</a>is 8.</p>
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<p><strong>Step 2:</strong>Now find n whose square is<a>less than</a>or equal to 33. We can say n is '5' because 5 x 5 = 25, which is less than 33. The<a>quotient</a>is 5 after subtracting 25 from 33, the<a>remainder</a>is 8.</p>
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<p><strong>Step 3:</strong>Bring down 60, making the new<a>dividend</a>860. Add the old<a>divisor</a>with the same number: 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 60, making the new<a>dividend</a>860. Add the old<a>divisor</a>with the same number: 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 10n 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 sum of the dividend and quotient. Now we get 10n 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 10n × n ≤ 860. Let us consider n as 8, now 108 x 8 = 864, which is greater than 860. Trying n as 7, we have 107 x 7 = 749.</p>
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<p><strong>Step 5:</strong>The next step is finding 10n × n ≤ 860. Let us consider n as 8, now 108 x 8 = 864, which is greater than 860. Trying n as 7, we have 107 x 7 = 749.</p>
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<p><strong>Step 6:</strong>Subtract 749 from 860, the difference is 111, and the quotient is 57.</p>
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<p><strong>Step 6:</strong>Subtract 749 from 860, the difference is 111, and the quotient is 57.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 11100.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 11100.</p>
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<p><strong>Step 8:</strong>Find the new divisor that is 579 because 5799 x 9 = 52191.</p>
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<p><strong>Step 8:</strong>Find the new divisor that is 579 because 5799 x 9 = 52191.</p>
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<p><strong>Step 9:</strong>Subtracting 52191 from 11100 results in 889.</p>
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<p><strong>Step 9:</strong>Subtracting 52191 from 11100 results in 889.</p>
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<p><strong>Step 10:</strong>Now the quotient is 57.9.</p>
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<p><strong>Step 10:</strong>Now the quotient is 57.9.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √3360 is approximately 57.93.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √3360 is approximately 57.93.</p>
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<h3>Square Root of 3360 by Approximation Method</h3>
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<h3>Square Root of 3360 by Approximation Method</h3>
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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. Let us learn how to find the square root of 3360 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. Let us learn how to find the square root of 3360 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √3360. The smallest perfect square less than 3360 is 3249 (57^2), and the largest perfect square more than 3360 is 3481 (59^2). √3360 falls between 57 and 59.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √3360. The smallest perfect square less than 3360 is 3249 (57^2), and the largest perfect square more than 3360 is 3481 (59^2). √3360 falls between 57 and 59.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Using the formula: (3360 - 3249) ÷ (3481 - 3249) = 111 ÷ 232 ≈ 0.4784 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the initial integer to the decimal number: 57 + 0.4784 ≈ 57.93. So the square root of 3360 is approximately 57.93.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Using the formula: (3360 - 3249) ÷ (3481 - 3249) = 111 ÷ 232 ≈ 0.4784 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the initial integer to the decimal number: 57 + 0.4784 ≈ 57.93. So the square root of 3360 is approximately 57.93.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3360</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 3360</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes that students make in detail.</p>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes that students 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 √3360?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √3360?</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 3360 square units.</p>
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<p>The area of the square is approximately 3360 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 √3360.</p>
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<p>The side length is given as √3360.</p>
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<p>Area of the square = side^2 = √3360 x √3360 = 3360.</p>
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<p>Area of the square = side^2 = √3360 x √3360 = 3360.</p>
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<p>Therefore, the area of the square box is approximately 3360 square units.</p>
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<p>Therefore, the area of the square box is approximately 3360 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 3360 square feet is built; if each of the sides is √3360, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 3360 square feet is built; if each of the sides is √3360, 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>1680 square feet</p>
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<p>1680 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can divide the given area by 2, as the building is square-shaped.</p>
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<p>We can divide the given area by 2, as the building is square-shaped.</p>
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<p>Dividing 3360 by 2 = 1680.</p>
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<p>Dividing 3360 by 2 = 1680.</p>
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<p>So half of the building measures 1680 square feet.</p>
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<p>So half of the building measures 1680 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 √3360 x 5.</p>
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<p>Calculate √3360 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>Approximately 289.66</p>
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<p>Approximately 289.66</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 3360, which is approximately 57.93.</p>
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<p>First, find the square root of 3360, which is approximately 57.93.</p>
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<p>The second step is to multiply 57.93 by 5.</p>
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<p>The second step is to multiply 57.93 by 5.</p>
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<p>So 57.93 x 5 ≈ 289.66.</p>
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<p>So 57.93 x 5 ≈ 289.66.</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 (3300 + 60)?</p>
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<p>What will be the square root of (3300 + 60)?</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 58.</p>
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<p>The square root is approximately 58.</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, find the sum of (3300 + 60).</p>
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<p>To find the square root, find the sum of (3300 + 60).</p>
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<p>3300 + 60 = 3360, and the square root of 3360 is approximately 58.</p>
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<p>3300 + 60 = 3360, and the square root of 3360 is approximately 58.</p>
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<p>Therefore, the square root of (3300 + 60) is approximately 58.</p>
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<p>Therefore, the square root of (3300 + 60) is approximately 58.</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 √3360 units and the width ‘w’ is 60 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √3360 units and the width ‘w’ is 60 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 235.86 units.</p>
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<p>The perimeter of the rectangle is approximately 235.86 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 × (√3360 + 60) Perimeter = 2 × (57.93 + 60) = 2 × 117.93 ≈ 235.86 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√3360 + 60) Perimeter = 2 × (57.93 + 60) = 2 × 117.93 ≈ 235.86 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 3360</h2>
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<h2>FAQ on Square Root of 3360</h2>
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<h3>1.What is √3360 in its simplest form?</h3>
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<h3>1.What is √3360 in its simplest form?</h3>
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<p>The prime factorization of 3360 is 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7. The simplest form of √3360 is √(2^4 x 3 x 5 x 7^2).</p>
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<p>The prime factorization of 3360 is 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7. The simplest form of √3360 is √(2^4 x 3 x 5 x 7^2).</p>
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<h3>2.Mention the factors of 3360.</h3>
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<h3>2.Mention the factors of 3360.</h3>
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<p>Factors of 3360 include 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 672, 840, 1120, 1680, and 3360.</p>
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<p>Factors of 3360 include 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 672, 840, 1120, 1680, and 3360.</p>
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<h3>3.Calculate the square of 3360.</h3>
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<h3>3.Calculate the square of 3360.</h3>
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<p>We get the square of 3360 by multiplying the number by itself, that is 3360 x 3360 = 11,289,600.</p>
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<p>We get the square of 3360 by multiplying the number by itself, that is 3360 x 3360 = 11,289,600.</p>
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<h3>4.Is 3360 a prime number?</h3>
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<h3>4.Is 3360 a prime number?</h3>
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<p>3360 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>3360 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.3360 is divisible by?</h3>
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<h3>5.3360 is divisible by?</h3>
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<p>3360 has many factors, including 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 672, 840, 1120, 1680, and 3360.</p>
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<p>3360 has many factors, including 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 672, 840, 1120, 1680, and 3360.</p>
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<h2>Important Glossaries for the Square Root of 3360</h2>
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<h2>Important Glossaries for the Square Root of 3360</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4.<strong></strong></li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4.<strong></strong></li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction, meaning it cannot be written in the form of p/q, where p and q are integers and q ≠ 0.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction, meaning it cannot be written in the form of p/q, where p and q are integers and q ≠ 0.</li>
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</ul><ul><li><strong>Principal square root:</strong>The positive square root of a number, which is used in most practical applications. It is the most commonly referenced square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>The positive square root of a number, which is used in most practical applications. It is the most commonly referenced square root.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.<strong></strong></li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.<strong></strong></li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of a number that is not a perfect square, involving a series of steps to approximate the root.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of a number that is not a perfect square, involving a series of steps to approximate the root.</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>