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2026-01-01
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2026-02-28
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<p>273 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 2450.</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 2450.</p>
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<h2>What is the Square Root of 2450?</h2>
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<h2>What is the Square Root of 2450?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 2450 is not a<a>perfect square</a>. The square root of 2450 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √2450, whereas (2450)^(1/2) in the exponential form. √2450 ≈ 49.4975, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 2450 is not a<a>perfect square</a>. The square root of 2450 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √2450, whereas (2450)^(1/2) in the exponential form. √2450 ≈ 49.4975, 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 2450</h2>
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<h2>Finding the Square Root of 2450</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><h2>Square Root of 2450 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 2450 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 2450 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 2450 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2450 Breaking it down, we get 2 x 5 x 5 x 7 x 7: 2^1 x 5^2 x 7^2</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 2450 Breaking it down, we get 2 x 5 x 5 x 7 x 7: 2^1 x 5^2 x 7^2</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 2450. The second step is to make pairs of those prime factors. Since 2450 is not a perfect square, therefore the digits of the number can’t be grouped into perfect pairs for all factors. However, we can simplify it to 5 x 7 √2 or 35√2.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 2450. The second step is to make pairs of those prime factors. Since 2450 is not a perfect square, therefore the digits of the number can’t be grouped into perfect pairs for all factors. However, we can simplify it to 5 x 7 √2 or 35√2.</p>
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<h2>Square Root of 2450 by Long Division Method</h2>
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<h2>Square Root of 2450 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 2450, we need to group it as 50 and 24.</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 2450, we need to group it as 50 and 24.</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 24. We can say n is ‘4’ because 4 x 4 = 16 is less than 24. Now the<a>quotient</a>is 4 after subtracting 24 - 16, the<a>remainder</a>is 8.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 24. We can say n is ‘4’ because 4 x 4 = 16 is less than 24. Now the<a>quotient</a>is 4 after subtracting 24 - 16, the<a>remainder</a>is 8.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be in the form of 8n. We need to find the value of n such that 8n x n ≤ 850. Let us consider n as 9, now 89 x 9 = 801.</p>
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<p><strong>Step 4:</strong>The new divisor will be in the form of 8n. We need to find the value of n such that 8n x n ≤ 850. Let us consider n as 9, now 89 x 9 = 801.</p>
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<p><strong>Step 5:</strong>Subtract 850 from 801, the difference is 49, and the quotient is 49.</p>
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<p><strong>Step 5:</strong>Subtract 850 from 801, the difference is 49, and the quotient is 49.</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 4900.</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 4900.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Let’s try 495, because 495 x 9 = 4455.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Let’s try 495, because 495 x 9 = 4455.</p>
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<p><strong>Step 8:</strong>Subtracting 4455 from 4900 gives us 445.</p>
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<p><strong>Step 8:</strong>Subtracting 4455 from 4900 gives us 445.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p>So the square root of √2450 is approximately 49.50.</p>
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<p>So the square root of √2450 is approximately 49.50.</p>
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<h2>Square Root of 2450 by Approximation Method</h2>
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<h2>Square Root of 2450 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2450 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2450 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √2450. The smallest perfect square less than 2450 is 2401 (49^2) and the largest perfect square<a>greater than</a>2450 is 2500 (50^2). √2450 falls somewhere between 49 and 50.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √2450. The smallest perfect square less than 2450 is 2401 (49^2) and the largest perfect square<a>greater than</a>2450 is 2500 (50^2). √2450 falls somewhere between 49 and 50.</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).</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).</p>
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<p>Using the formula (2450 - 2401) ÷ (2500 - 2401) = 49 / 99 ≈ 0.4949. Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>Using the formula (2450 - 2401) ÷ (2500 - 2401) = 49 / 99 ≈ 0.4949. Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 49 + 0.4949 ≈ 49.50, so the square root of 2450 is approximately 49.50.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 49 + 0.4949 ≈ 49.50, so the square root of 2450 is approximately 49.50.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2450</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 2450</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping methods like long division. 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 or skipping methods like long division. 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 √2450?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √2450?</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 2450 square units.</p>
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<p>The area of the square is 2450 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 √2450.</p>
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<p>The side length is given as √2450.</p>
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<p>Area of the square = side² = √2450 x √2450 = 2450.</p>
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<p>Area of the square = side² = √2450 x √2450 = 2450.</p>
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<p>Therefore, the area of the square box is 2450 square units.</p>
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<p>Therefore, the area of the square box is 2450 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 2450 square feet is built; if each of the sides is √2450, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 2450 square feet is built; if each of the sides is √2450, 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>1225 square feet</p>
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<p>1225 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 2450 by 2, we get 1225.</p>
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<p>Dividing 2450 by 2, we get 1225.</p>
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<p>So half of the building measures 1225 square feet.</p>
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<p>So half of the building measures 1225 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 √2450 x 5.</p>
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<p>Calculate √2450 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 247.49</p>
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<p>Approximately 247.49</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 2450, which is approximately 49.50.</p>
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<p>The first step is to find the square root of 2450, which is approximately 49.50.</p>
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<p>The second step is to multiply 49.50 with 5.</p>
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<p>The second step is to multiply 49.50 with 5.</p>
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<p>So 49.50 x 5 ≈ 247.49.</p>
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<p>So 49.50 x 5 ≈ 247.49.</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 (2450 + 50)?</p>
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<p>What will be the square root of (2450 + 50)?</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 50.</p>
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<p>The square root is 50.</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 (2450 + 50).</p>
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<p>To find the square root, we need to find the sum of (2450 + 50).</p>
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<p>2450 + 50 = 2500, and then √2500 = 50.</p>
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<p>2450 + 50 = 2500, and then √2500 = 50.</p>
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<p>Therefore, the square root of (2450 + 50) is ±50.</p>
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<p>Therefore, the square root of (2450 + 50) is ±50.</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 √2450 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 √2450 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 approximately 175.99 units.</p>
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<p>We find the perimeter of the rectangle as approximately 175.99 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 × (√2450 + 38) = 2 × (49.50 + 38) ≈ 2 × 87.50 = 175.99 units.</p>
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<p>Perimeter = 2 × (√2450 + 38) = 2 × (49.50 + 38) ≈ 2 × 87.50 = 175.99 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 2450</h2>
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<h2>FAQ on Square Root of 2450</h2>
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<h3>1.What is √2450 in its simplest form?</h3>
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<h3>1.What is √2450 in its simplest form?</h3>
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<p>The prime factorization of 2450 is 2 x 5 x 5 x 7 x 7, so the simplest form of √2450 = √(2 x 5^2 x 7^2) = 35√2.</p>
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<p>The prime factorization of 2450 is 2 x 5 x 5 x 7 x 7, so the simplest form of √2450 = √(2 x 5^2 x 7^2) = 35√2.</p>
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<h3>2.Mention the factors of 2450.</h3>
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<h3>2.Mention the factors of 2450.</h3>
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<p>Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 490, 1225, and 2450.</p>
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<p>Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 490, 1225, and 2450.</p>
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<h3>3.Calculate the square of 2450.</h3>
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<h3>3.Calculate the square of 2450.</h3>
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<p>We get the square of 2450 by multiplying the number by itself, that is 2450 x 2450 = 6,002,500.</p>
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<p>We get the square of 2450 by multiplying the number by itself, that is 2450 x 2450 = 6,002,500.</p>
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<h3>4.Is 2450 a prime number?</h3>
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<h3>4.Is 2450 a prime number?</h3>
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<p>2450 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>2450 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.2450 is divisible by?</h3>
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<h3>5.2450 is divisible by?</h3>
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<p>2450 has many factors; those are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 490, 1225, and 2450.</p>
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<p>2450 has many factors; those are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 490, 1225, and 2450.</p>
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<h2>Important Glossaries for the Square Root of 2450</h2>
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<h2>Important Glossaries for the Square Root of 2450</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 7^2 = 49, and the inverse of the square is the square root, that is √49 = 7.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 7^2 = 49, and the inverse of the square is the square root, that is √49 = 7.</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 a 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 a principal square root.</li>
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</ul><ul><li><strong>Approximation:</strong>The method of finding a value that is close enough to the right answer, usually within an acceptable range or tolerance.</li>
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</ul><ul><li><strong>Approximation:</strong>The method of finding a value that is close enough to the right answer, usually within an acceptable range or tolerance.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Decomposing a composite number into a product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Decomposing a composite number into a product of its prime factors.</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>