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2026-01-01
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2026-02-28
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<p>241 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 490.</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 490.</p>
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<h2>What is the Square Root of 490?</h2>
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<h2>What is the Square Root of 490?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 490 is not a<a>perfect square</a>. The square root of 490 is expressed in both radical and exponential forms.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 490 is not a<a>perfect square</a>. The square root of 490 is expressed in both radical and exponential forms.</p>
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<p>In the radical form, it is expressed as √490, whereas (490)^(1/2) in the<a>exponential form</a>. √490 = 22.13594362, 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>In the radical form, it is expressed as √490, whereas (490)^(1/2) in the<a>exponential form</a>. √490 = 22.13594362, 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 490</h2>
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<h2>Finding the Square Root of 490</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<a>long division</a>method and approximation method are used. Let us now learn the following methods: Prime factorization method Long division method Approximation method</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<a>long division</a>method and approximation method are used. Let us now learn the following methods: Prime factorization method Long division method Approximation method</p>
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<h2>Square Root of 490 by Prime Factorization Method</h2>
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<h2>Square Root of 490 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 490 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 490 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 490</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 490</p>
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<p>Breaking it down, we get 2 x 5 x 7 x 7: 2^1 x 5^1 x 7^2</p>
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<p>Breaking it down, we get 2 x 5 x 7 x 7: 2^1 x 5^1 x 7^2</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 490. Since 490 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 490 using prime factorization is not straightforward for finding an exact<a>square root</a>.</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 490. Since 490 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 490 using prime factorization is not straightforward for finding an exact<a>square root</a>.</p>
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<h2>Square Root of 490 by Long Division Method</h2>
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<h2>Square Root of 490 by Long Division Method</h2>
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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 square root 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 square root 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 490, we need to group it as 90 and 4.</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 490, we need to group it as 90 and 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 4. Now the<a>quotient</a>is 2 after subtracting 4-4 the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 4. Now the<a>quotient</a>is 2 after subtracting 4-4 the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 90 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 90 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 90. Let us consider n as 2. Now 4 x 2 x 2 = 8 x 2 = 16</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 90. Let us consider n as 2. Now 4 x 2 x 2 = 8 x 2 = 16</p>
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<p><strong>Step 6:</strong>Subtract 90 from 16, the difference is 74, and the quotient is 22</p>
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<p><strong>Step 6:</strong>Subtract 90 from 16, the difference is 74, and the quotient is 22</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7400.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 445 because 445 x 5 = 2225</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 445 because 445 x 5 = 2225</p>
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<p><strong>Step 9:</strong>Subtracting 2225 from 7400, we get the result 5175.</p>
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<p><strong>Step 9:</strong>Subtracting 2225 from 7400, we get the result 5175.</p>
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<p><strong>Step 10:</strong>Now the quotient is 22.1</p>
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<p><strong>Step 10:</strong>Now the quotient is 22.1</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.</p>
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<p>So the square root of √490 is approximately 22.13.</p>
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<p>So the square root of √490 is approximately 22.13.</p>
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<h2>Square Root of 490 by Approximation Method</h2>
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<h2>Square Root of 490 by Approximation Method</h2>
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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 490 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 490 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √490. The smallest perfect square less than 490 is 484 and the largest perfect square<a>greater than</a>490 is 529. √490 falls somewhere between 22 and 23.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √490. The smallest perfect square less than 490 is 484 and the largest perfect square<a>greater than</a>490 is 529. √490 falls somewhere between 22 and 23.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (490 - 484) / (529 - 484) = 6/45 ≈ 0.1333</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (490 - 484) / (529 - 484) = 6/45 ≈ 0.1333</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 22 + 0.1333 = 22.1333, so the square root of 490 is approximately 22.13.</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 22 + 0.1333 = 22.1333, so the square root of 490 is approximately 22.13.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 490</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 490</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 √490?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √490?</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 490 square units.</p>
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<p>The area of the square is 490 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 √490.</p>
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<p>The side length is given as √490.</p>
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<p>Area of the square = side^2 = √490 x √490 = 490.</p>
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<p>Area of the square = side^2 = √490 x √490 = 490.</p>
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<p>Therefore, the area of the square box is 490 square units.</p>
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<p>Therefore, the area of the square box is 490 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 490 square feet is built; if each of the sides is √490, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 490 square feet is built; if each of the sides is √490, 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>245 square feet</p>
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<p>245 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 490 by 2 = we get 245.</p>
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<p>Dividing 490 by 2 = we get 245.</p>
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<p>So half of the building measures 245 square feet.</p>
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<p>So half of the building measures 245 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 √490 x 5.</p>
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<p>Calculate √490 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>110.6797181</p>
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<p>110.6797181</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 490, which is approximately 22.13594362.</p>
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<p>The first step is to find the square root of 490, which is approximately 22.13594362.</p>
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<p>The second step is to multiply 22.13594362 with 5.</p>
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<p>The second step is to multiply 22.13594362 with 5.</p>
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<p>So 22.13594362 x 5 = 110.6797181.</p>
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<p>So 22.13594362 x 5 = 110.6797181.</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 (484 + 6)?</p>
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<p>What will be the square root of (484 + 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 approximately 22.13594362</p>
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<p>The square root is approximately 22.13594362</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 (484 + 6). 484 + 6 = 490, and then √490 = approximately 22.13594362.</p>
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<p>To find the square root, we need to find the sum of (484 + 6). 484 + 6 = 490, and then √490 = approximately 22.13594362.</p>
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<p>Therefore, the square root of (484 + 6) is approximately ±22.13594362.</p>
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<p>Therefore, the square root of (484 + 6) is approximately ±22.13594362.</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 √490 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 √490 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 120.2718872 units.</p>
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<p>We find the perimeter of the rectangle as 120.2718872 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 × (√490 + 38) = 2 × (22.13594362 + 38) = 2 × 60.13594362 = 120.2718872 units.</p>
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<p>Perimeter = 2 × (√490 + 38) = 2 × (22.13594362 + 38) = 2 × 60.13594362 = 120.2718872 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 490</h2>
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<h2>FAQ on Square Root of 490</h2>
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<h3>1.What is √490 in its simplest form?</h3>
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<h3>1.What is √490 in its simplest form?</h3>
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<p>The prime factorization of 490 is 2 x 5 x 7 x 7, so the simplest form of √490 is √(2 x 5 x 7^2) = 7√(10).</p>
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<p>The prime factorization of 490 is 2 x 5 x 7 x 7, so the simplest form of √490 is √(2 x 5 x 7^2) = 7√(10).</p>
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<h3>2.Mention the factors of 490.</h3>
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<h3>2.Mention the factors of 490.</h3>
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<p>Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.</p>
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<p>Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.</p>
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<h3>3.Calculate the square of 490.</h3>
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<h3>3.Calculate the square of 490.</h3>
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<p>We get the square of 490 by multiplying the number by itself, that is 490 x 490 = 240100.</p>
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<p>We get the square of 490 by multiplying the number by itself, that is 490 x 490 = 240100.</p>
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<h3>4.Is 490 a prime number?</h3>
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<h3>4.Is 490 a prime number?</h3>
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<h3>5.490 is divisible by?</h3>
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<h3>5.490 is divisible by?</h3>
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<p>490 has many factors; those are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.</p>
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<p>490 has many factors; those are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.</p>
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<h2>Important Glossaries for the Square Root of 490</h2>
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<h2>Important Glossaries for the Square Root of 490</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>Exponent:</strong>An exponent represents the number of times a base number is multiplied by itself. For example: 2^3 = 2 x 2 x 2 = 8. </li>
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<li><strong>Exponent:</strong>An exponent represents the number of times a base number is multiplied by itself. For example: 2^3 = 2 x 2 x 2 = 8. </li>
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<li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors. For example, the prime factorization of 50 is 2 x 5 x 5. </li>
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<li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors. For example, the prime factorization of 50 is 2 x 5 x 5. </li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example: 9 is a perfect square because it is 3^2.</li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example: 9 is a perfect square because it is 3^2.</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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<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>