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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 100000.</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 100000.</p>
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<h2>What is the Square Root of 100000?</h2>
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<h2>What is the Square Root of 100000?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 100000 is not a<a>perfect square</a>. The square root of 100000 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √100000, whereas (100000)^(1/2) in the exponential form. √100000 = 316.227766, 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>. 100000 is not a<a>perfect square</a>. The square root of 100000 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √100000, whereas (100000)^(1/2) in the exponential form. √100000 = 316.227766, 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 100000</h2>
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<h2>Finding the Square Root of 100000</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><h2>Square Root of 100000 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 100000 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 100000 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 100000 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 100000 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5:<a>2^5</a>x 5^4</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 100000 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5:<a>2^5</a>x 5^4</p>
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<p><strong>Step 2:</strong>Now that we have found the prime factors of 100000, the second step is to make pairs of those prime factors.</p>
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<p><strong>Step 2:</strong>Now that we have found the prime factors of 100000, the second step is to make pairs of those prime factors.</p>
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<p>Since 100000 is not a perfect square, calculating its<a>square root</a>using prime factorization directly is not feasible.</p>
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<p>Since 100000 is not a perfect square, calculating its<a>square root</a>using prime factorization directly is not feasible.</p>
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<h2>Square Root of 100000 by Long Division Method</h2>
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<h2>Square Root of 100000 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 square root 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 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 100000, we need to group it as 00, 00, and 10.</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 100000, we need to group it as 00, 00, and 10.</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 10. We can say n is ‘3’ because 3 × 3 = 9, which is less than 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</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 10. We can say n is ‘3’ because 3 × 3 = 9, which is less than 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits (00) to the right of the remainder, making it 100.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits (00) to the right of the remainder, making it 100.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>will be the<a>sum</a>of the old divisor and the quotient, which is 6 (3 + 3). Now we need to find n such that 6n × n ≤ 100.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>will be the<a>sum</a>of the old divisor and the quotient, which is 6 (3 + 3). Now we need to find n such that 6n × n ≤ 100.</p>
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<p><strong>Step 5:</strong>Let n be 1, then 61 × 1 = 61, and subtract 61 from 100 to get 39.</p>
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<p><strong>Step 5:</strong>Let n be 1, then 61 × 1 = 61, and subtract 61 from 100 to get 39.</p>
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<p><strong>Step 6:</strong>Bring down the next pair of digits (00) to make it 3900.</p>
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<p><strong>Step 6:</strong>Bring down the next pair of digits (00) to make it 3900.</p>
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<p><strong>Step 7:</strong>The new divisor is 62 (61 + 1), and we need to find n such that 62n × n ≤ 3900.</p>
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<p><strong>Step 7:</strong>The new divisor is 62 (61 + 1), and we need to find n such that 62n × n ≤ 3900.</p>
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<p><strong>Step 8:</strong>Let n be 6, then 626 × 6 = 3756, and subtract 3756 from 3900 to get 144.</p>
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<p><strong>Step 8:</strong>Let n be 6, then 626 × 6 = 3756, and subtract 3756 from 3900 to get 144.</p>
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<p><strong>Step 9:</strong>Add a<a>decimal</a>point and bring down two zeros, making it 14400.</p>
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<p><strong>Step 9:</strong>Add a<a>decimal</a>point and bring down two zeros, making it 14400.</p>
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<p><strong>Step 10:</strong>Continue this process until you reach the desired decimal places.</p>
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<p><strong>Step 10:</strong>Continue this process until you reach the desired decimal places.</p>
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<p>So the square root of √100000 is approximately 316.2277.</p>
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<p>So the square root of √100000 is approximately 316.2277.</p>
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<h2>Square Root of 100000 by Approximation Method</h2>
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<h2>Square Root of 100000 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 100000 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 100000 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √100000. The smallest perfect square less than 100000 is 96100 (310^2), and the largest perfect square<a>greater than</a>100000 is 102400 (320^2). √100000 falls somewhere between 310 and 320.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √100000. The smallest perfect square less than 100000 is 96100 (310^2), and the largest perfect square<a>greater than</a>100000 is 102400 (320^2). √100000 falls somewhere between 310 and 320.</p>
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<p><strong>Step 2:</strong>Now we need to estimate the value between these two perfect squares. We can see that 100000 is closer to 102400 than it is to 96100, so a value closer to 316 is reasonable.</p>
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<p><strong>Step 2:</strong>Now we need to estimate the value between these two perfect squares. We can see that 100000 is closer to 102400 than it is to 96100, so a value closer to 316 is reasonable.</p>
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<p><strong>Step 3:</strong>Using the approximation, we find the square root of 100000 to be approximately 316.2277.</p>
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<p><strong>Step 3:</strong>Using the approximation, we find the square root of 100000 to be approximately 316.2277.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 100000</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 100000</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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, like forgetting about the negative square root or skipping long division methods. 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 length of a side of a square field if its area is 100000 square meters?</p>
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<p>Can you help Max find the length of a side of a square field if its area is 100000 square meters?</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 length of a side of the square field is approximately 316.23 meters.</p>
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<p>The length of a side of the square field is approximately 316.23 meters.</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> If the area is 100000 square meters, then the side length = √100000 ≈ 316.23 meters.</p>
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<p> If the area is 100000 square meters, then the side length = √100000 ≈ 316.23 meters.</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 100000 square feet is built; if each of the sides is √100000, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 100000 square feet is built; if each of the sides is √100000, 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>50000 square feet</p>
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<p>50000 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 100000 by 2 gives us 50000.</p>
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<p>Dividing 100000 by 2 gives us 50000.</p>
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<p>So half of the building measures 50000 square feet.</p>
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<p>So half of the building measures 50000 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 √100000 x 5.</p>
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<p>Calculate √100000 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>1581.14</p>
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<p>1581.14</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 100000, which is approximately 316.23.</p>
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<p>The first step is to find the square root of 100000, which is approximately 316.23.</p>
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<p>The second step is to multiply 316.23 by 5.</p>
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<p>The second step is to multiply 316.23 by 5.</p>
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<p>So 316.23 x 5 = 1581.14.</p>
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<p>So 316.23 x 5 = 1581.14.</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 (100000 + 2400)?</p>
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<p>What will be the square root of (100000 + 2400)?</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 320.</p>
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<p>The square root is approximately 320.</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 (100000 + 2400).</p>
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<p>To find the square root, we need to find the sum of (100000 + 2400).</p>
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<p>100000 + 2400 = 102400, and then √102400 = 320.</p>
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<p>100000 + 2400 = 102400, and then √102400 = 320.</p>
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<p>Therefore, the square root of (100000 + 2400) is ±320.</p>
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<p>Therefore, the square root of (100000 + 2400) is ±320.</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 √100000 units and the width ‘w’ is 50 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √100000 units and the width ‘w’ is 50 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 732.46 units.</p>
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<p>We find the perimeter of the rectangle as approximately 732.46 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 × (√100000 + 50)</p>
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<p>Perimeter = 2 × (√100000 + 50)</p>
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<p>= 2 × (316.23 + 50)</p>
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<p>= 2 × (316.23 + 50)</p>
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<p>= 2 × 366.23</p>
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<p>= 2 × 366.23</p>
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<p>= 732.46 units.</p>
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<p>= 732.46 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 100000</h2>
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<h2>FAQ on Square Root of 100000</h2>
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<h3>1.What is √100000 in its simplest form?</h3>
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<h3>1.What is √100000 in its simplest form?</h3>
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<p>The prime factorization of 100000 is 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.</p>
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<p>The prime factorization of 100000 is 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.</p>
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<p>So the simplest form of √100000 = √(2^5 x 5^4).</p>
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<p>So the simplest form of √100000 = √(2^5 x 5^4).</p>
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<h3>2.Mention the factors of 100000.</h3>
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<h3>2.Mention the factors of 100000.</h3>
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<p>Factors of 100000 include 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.</p>
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<p>Factors of 100000 include 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.</p>
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<h3>3.Calculate the square of 100000.</h3>
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<h3>3.Calculate the square of 100000.</h3>
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<p>We get the square of 100000 by multiplying the number by itself, which is 100000 x 100000 = 10000000000.</p>
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<p>We get the square of 100000 by multiplying the number by itself, which is 100000 x 100000 = 10000000000.</p>
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<h3>4.Is 100000 a prime number?</h3>
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<h3>4.Is 100000 a prime number?</h3>
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<p>100000 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>100000 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.100000 is divisible by?</h3>
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<h3>5.100000 is divisible by?</h3>
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<p>100000 is divisible by factors such as 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.</p>
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<p>100000 is divisible by factors such as 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.</p>
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<h2>Important Glossaries for the Square Root of 100000</h2>
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<h2>Important Glossaries for the Square Root of 100000</h2>
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<ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. </li>
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<ul><li><strong>Square root:</strong>A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; its decimal goes on forever without repeating. √100000 is irrational. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction; its decimal goes on forever without repeating. √100000 is irrational. </li>
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<li><strong>Principal square root:</strong>This refers to the positive square root of a number. For example, the principal square root of 100000 is approximately 316.23. </li>
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<li><strong>Principal square root:</strong>This refers to the positive square root of a number. For example, the principal square root of 100000 is approximately 316.23. </li>
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<li><strong>Prime factorization:</strong>A way of expressing a number as the product of its prime factors. For instance, the prime factorization of 100000 is 2^5 × 5^4. </li>
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<li><strong>Prime factorization:</strong>A way of expressing a number as the product of its prime factors. For instance, the prime factorization of 100000 is 2^5 × 5^4. </li>
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<li><strong>Perimeter:</strong>The total length around a two-dimensional shape. For example, the perimeter of a rectangle is calculated as 2 × (length + width).</li>
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<li><strong>Perimeter:</strong>The total length around a two-dimensional shape. For example, the perimeter of a rectangle is calculated as 2 × (length + width).</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>