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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1170.</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 1170.</p>
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<h2>What is the Square Root of 1170?</h2>
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<h2>What is the Square Root of 1170?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 1170 is not a<a>perfect square</a>. The square root of 1170 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1170, whereas (1170)^(1/2) in the<a>exponential form</a>. √1170 ≈ 34.224, 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 a<a>number</a>. 1170 is not a<a>perfect square</a>. The square root of 1170 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1170, whereas (1170)^(1/2) in the<a>exponential form</a>. √1170 ≈ 34.224, 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 1170</h2>
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<h2>Finding the Square Root of 1170</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the<a>long 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, for non-perfect square numbers, the<a>long 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 1170 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 1170 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 1170 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 1170 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1170 Breaking it down, we get 2 x 3 x 3 x 5 x 13: 2^1 x 3^2 x 5^1 x 13^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1170 Breaking it down, we get 2 x 3 x 3 x 5 x 13: 2^1 x 3^2 x 5^1 x 13^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1170. The second step is to make pairs of those prime factors. Since 1170 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1170 using prime factorization is not straightforward.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1170. The second step is to make pairs of those prime factors. Since 1170 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1170 using prime factorization is not straightforward.</p>
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<h3>Square Root of 1170 by Long Division Method</h3>
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<h3>Square Root of 1170 by Long Division Method</h3>
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<p>The long<a>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 long<a>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 1170, we need to group it as 70 and 11.</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 1170, we need to group it as 70 and 11.</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 11. We can say n is '3' because 3 x 3 = 9, which is less than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.</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 11. We can say n is '3' because 3 x 3 = 9, which is less than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 70, making the new<a>dividend</a>270. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 70, making the new<a>dividend</a>270. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>We need to find a digit n such that 6n x n is less than or equal to 270. Let us consider n as 4, then 6 x 4 x 4 = 256.</p>
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<p><strong>Step 4:</strong>We need to find a digit n such that 6n x n is less than or equal to 270. Let us consider n as 4, then 6 x 4 x 4 = 256.</p>
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<p><strong>Step 5:</strong>Subtract 256 from 270, the difference is 14, and the quotient is 34.</p>
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<p><strong>Step 5:</strong>Subtract 256 from 270, the difference is 14, and the quotient is 34.</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 1400.</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 1400.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 688, because 688 x 2 = 1376.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 688, because 688 x 2 = 1376.</p>
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<p><strong>Step 8:</strong>Subtracting 1376 from 1400 gives the result 24.</p>
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<p><strong>Step 8:</strong>Subtracting 1376 from 1400 gives the result 24.</p>
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<p><strong>Step 9:</strong>Now the quotient is 34.2.</p>
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<p><strong>Step 9:</strong>Now the quotient is 34.2.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p>So the square root of √1170 is approximately 34.22.</p>
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<p>So the square root of √1170 is approximately 34.22.</p>
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<h3>Square Root of 1170 by Approximation Method</h3>
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<h3>Square Root of 1170 by Approximation Method</h3>
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<p>The approximation method is another method for finding 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 1170 using the approximation method.</p>
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<p>The approximation method is another method for finding 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 1170 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1170. The smallest perfect square less than 1170 is 1156, and the largest perfect square<a>greater than</a>1170 is 1225. √1170 falls somewhere between 34 and 35.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1170. The smallest perfect square less than 1170 is 1156, and the largest perfect square<a>greater than</a>1170 is 1225. √1170 falls somewhere between 34 and 35.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greatest perfect square - smallest perfect square). Using the formula: (1170 - 1156) ÷ (1225 - 1156) = 14 ÷ 69 ≈ 0.2029 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 34 + 0.2029 ≈ 34.2, so the square root of 1170 is approximately 34.2.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greatest perfect square - smallest perfect square). Using the formula: (1170 - 1156) ÷ (1225 - 1156) = 14 ÷ 69 ≈ 0.2029 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 34 + 0.2029 ≈ 34.2, so the square root of 1170 is approximately 34.2.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1170</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1170</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 √1170?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1170?</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 1367.376 square units.</p>
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<p>The area of the square is approximately 1367.376 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 √1170.</p>
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<p>The side length is given as √1170.</p>
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<p>Area of the square = side^2 = √1170 x √1170 ≈ 34.224 x 34.224 ≈ 1367.376.</p>
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<p>Area of the square = side^2 = √1170 x √1170 ≈ 34.224 x 34.224 ≈ 1367.376.</p>
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<p>Therefore, the area of the square box is approximately 1367.376 square units.</p>
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<p>Therefore, the area of the square box is approximately 1367.376 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 1170 square feet is built; if each of the sides is √1170, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1170 square feet is built; if each of the sides is √1170, 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>585 square feet</p>
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<p>585 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 1170 by 2, we get 585.</p>
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<p>Dividing 1170 by 2, we get 585.</p>
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<p>So half of the building measures 585 square feet.</p>
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<p>So half of the building measures 585 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 √1170 x 5.</p>
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<p>Calculate √1170 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>171.12</p>
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<p>171.12</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 1170, which is approximately 34.224. The second step is to multiply 34.224 with 5. So 34.224 x 5 ≈ 171.12.</p>
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<p>The first step is to find the square root of 1170, which is approximately 34.224. The second step is to multiply 34.224 with 5. So 34.224 x 5 ≈ 171.12.</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 (1156 + 14)?</p>
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<p>What will be the square root of (1156 + 14)?</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 34.</p>
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<p>The square root is 34.</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 (1156 + 14). 1156 + 14 = 1170, and then √1170 ≈ 34.224. Therefore, the square root of (1156 + 14) is approximately ±34.224.</p>
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<p>To find the square root, we need to find the sum of (1156 + 14). 1156 + 14 = 1170, and then √1170 ≈ 34.224. Therefore, the square root of (1156 + 14) is approximately ±34.224.</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 √1170 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 √1170 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 128.448 units.</p>
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<p>We find the perimeter of the rectangle as approximately 128.448 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 × (√1170 + 30) ≈ 2 × (34.224 + 30) ≈ 2 × 64.224 ≈ 128.448 units.</p>
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<p>Perimeter = 2 × (√1170 + 30) ≈ 2 × (34.224 + 30) ≈ 2 × 64.224 ≈ 128.448 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 1170</h2>
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<h2>FAQ on Square Root of 1170</h2>
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<h3>1.What is √1170 in its simplest form?</h3>
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<h3>1.What is √1170 in its simplest form?</h3>
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<p>The prime factorization of 1170 is 2 x 3 x 3 x 5 x 13, so the simplest form of √1170 = √(2 x 3^2 x 5 x 13).</p>
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<p>The prime factorization of 1170 is 2 x 3 x 3 x 5 x 13, so the simplest form of √1170 = √(2 x 3^2 x 5 x 13).</p>
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<h3>2.Mention the factors of 1170.</h3>
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<h3>2.Mention the factors of 1170.</h3>
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<p>Factors of 1170 are 1, 2, 3, 5, 6, 9, 10, 13, 15, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.</p>
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<p>Factors of 1170 are 1, 2, 3, 5, 6, 9, 10, 13, 15, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.</p>
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<h3>3.Calculate the square of 1170.</h3>
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<h3>3.Calculate the square of 1170.</h3>
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<p>We get the square of 1170 by multiplying the number by itself, that is 1170 x 1170 = 1,368,900.</p>
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<p>We get the square of 1170 by multiplying the number by itself, that is 1170 x 1170 = 1,368,900.</p>
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<h3>4.Is 1170 a prime number?</h3>
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<h3>4.Is 1170 a prime number?</h3>
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<p>1170 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>1170 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1170 is divisible by?</h3>
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<h3>5.1170 is divisible by?</h3>
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<p>1170 has many factors; those are 1, 2, 3, 5, 6, 9, 10, 13, 15, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.</p>
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<p>1170 has many factors; those are 1, 2, 3, 5, 6, 9, 10, 13, 15, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, and 1170.</p>
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<h2>Important Glossaries for the Square Root of 1170</h2>
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<h2>Important Glossaries for the Square Root of 1170</h2>
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<ul><li><strong>Square root:</strong>The square root is the inverse of a square. For 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>The square root is the inverse of a square. For 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, 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 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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</ul><ul><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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</ul><ul><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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</ul><ul><li><strong>Long division method:</strong>A systematic approach used to find the square root of a non-perfect square by dividing in a step-by-step manner.</li>
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</ul><ul><li><strong>Long division method:</strong>A systematic approach used to find the square root of a non-perfect square by dividing in a step-by-step manner.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the square root of a non-perfect square by estimating its value based on nearby perfect squares.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the square root of a non-perfect square by estimating its value based on nearby 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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<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>