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Original
2026-01-01
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2026-02-28
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<p>220 Learners</p>
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<p>252 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 1049.</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 1049.</p>
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<h2>What is the Square Root of 1049?</h2>
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<h2>What is the Square Root of 1049?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1049 is not a<a>perfect square</a>. The square root of 1049 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1049, whereas 1049^(1/2) in the exponential form. √1049 ≈ 32.407, 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>. 1049 is not a<a>perfect square</a>. The square root of 1049 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1049, whereas 1049^(1/2) in the exponential form. √1049 ≈ 32.407, 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 1049</h2>
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<h2>Finding the Square Root of 1049</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 1049 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 1049 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 1049 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 1049 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1049. Since 1049 is a<a>prime number</a>itself, it cannot be broken down into smaller prime factors other than 1049 and 1.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1049. Since 1049 is a<a>prime number</a>itself, it cannot be broken down into smaller prime factors other than 1049 and 1.</p>
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<p><strong>Step 2:</strong>Since 1049 is not a perfect square, therefore, calculating 1049 using prime factorization to find its<a>square root</a>directly is not feasible.</p>
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<p><strong>Step 2:</strong>Since 1049 is not a perfect square, therefore, calculating 1049 using prime factorization to find its<a>square root</a>directly is not feasible.</p>
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<h2>Square Root of 1049 by Long Division Method</h2>
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<h2>Square Root of 1049 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>Group the digits in pairs from right to left. In the case of 1049, it is already a four-digit number, so we consider it as 10|49.</p>
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<p><strong>Step 1:</strong>Group the digits in pairs from right to left. In the case of 1049, it is already a four-digit number, so we consider it as 10|49.</p>
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<p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to the first group (10). The number is 3 because 3^2 = 9.</p>
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<p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to the first group (10). The number is 3 because 3^2 = 9.</p>
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<p><strong>Step 3:</strong>Subtract 9 from 10, leaving a<a>remainder</a>of 1. Bring down the next group of digits (49) to make the new<a>dividend</a>149.</p>
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<p><strong>Step 3:</strong>Subtract 9 from 10, leaving a<a>remainder</a>of 1. Bring down the next group of digits (49) to make the new<a>dividend</a>149.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>is twice the current<a>quotient</a>(3), which gives us 6. We need to find a digit n such that 6n × n ≤ 149.</p>
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<p><strong>Step 4:</strong>The new<a>divisor</a>is twice the current<a>quotient</a>(3), which gives us 6. We need to find a digit n such that 6n × n ≤ 149.</p>
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<p><strong>Step 5:</strong>n = 2 fits because 62 × 2 = 124.</p>
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<p><strong>Step 5:</strong>n = 2 fits because 62 × 2 = 124.</p>
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<p><strong>Step 6:</strong>Subtract 124 from 149 to get a remainder of 25. Now, bring down double zeros to make it 2500.</p>
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<p><strong>Step 6:</strong>Subtract 124 from 149 to get a remainder of 25. Now, bring down double zeros to make it 2500.</p>
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<p><strong>Step 7:</strong>Continue this process to find the next digits of the square root, adding a<a>decimal</a>point as necessary.</p>
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<p><strong>Step 7:</strong>Continue this process to find the next digits of the square root, adding a<a>decimal</a>point as necessary.</p>
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<p>After several iterations, the square root of 1049 is approximately 32.407.</p>
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<p>After several iterations, the square root of 1049 is approximately 32.407.</p>
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<h2>Square Root of 1049 by Approximation Method</h2>
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<h2>Square Root of 1049 by Approximation Method</h2>
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<p>The approximation method is another method for finding the 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 1049 using the approximation method.</p>
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<p>The approximation method is another method for finding the 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 1049 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 1049. The closest perfect square less than 1049 is 1024 (32^2), and the one greater is 1089 (33^2).</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares around 1049. The closest perfect square less than 1049 is 1024 (32^2), and the one greater is 1089 (33^2).</p>
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<p><strong>Step 2:</strong>Since 1049 is closer to 1024, we estimate that the square root of 1049 is slightly more than 32 but less than 33. Using linear approximation, we can find a more precise value.</p>
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<p><strong>Step 2:</strong>Since 1049 is closer to 1024, we estimate that the square root of 1049 is slightly more than 32 but less than 33. Using linear approximation, we can find a more precise value.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1049</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1049</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Let us look at a few common mistakes in detail.</p>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Let us look at a few common mistakes 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 √1049?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1049?</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 1049 square units.</p>
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<p>The area of the square is approximately 1049 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 √1049.</p>
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<p>The side length is given as √1049.</p>
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<p>Area of the square = side²</p>
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<p>Area of the square = side²</p>
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<p>= (√1049) × (√1049)</p>
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<p>= (√1049) × (√1049)</p>
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<p>= 1049.</p>
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<p>= 1049.</p>
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<p>Therefore, the area of the square box is approximately 1049 square units.</p>
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<p>Therefore, the area of the square box is approximately 1049 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 1049 square feet is built; if each of the sides is √1049, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1049 square feet is built; if each of the sides is √1049, 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>524.5 square feet</p>
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<p>524.5 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 1049 by 2 gives us 524.5.</p>
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<p>Dividing 1049 by 2 gives us 524.5.</p>
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<p>So half of the building measures 524.5 square feet.</p>
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<p>So half of the building measures 524.5 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 √1049 × 5.</p>
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<p>Calculate √1049 × 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 162.035</p>
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<p>Approximately 162.035</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 1049, which is approximately 32.407.</p>
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<p>First, find the square root of 1049, which is approximately 32.407.</p>
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<p>Then, multiply 32.407 by 5. So, 32.407 × 5 ≈ 162.035.</p>
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<p>Then, multiply 32.407 by 5. So, 32.407 × 5 ≈ 162.035.</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 (1000 + 49)?</p>
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<p>What will be the square root of (1000 + 49)?</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 32.407.</p>
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<p>The square root is approximately 32.407.</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, calculate the sum of (1000 + 49) which equals 1049.</p>
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<p>To find the square root, calculate the sum of (1000 + 49) which equals 1049.</p>
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<p>Then, the square root of 1049 is approximately 32.407.</p>
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<p>Then, the square root of 1049 is approximately 32.407.</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 √1049 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 √1049 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>The perimeter of the rectangle is approximately 140.814 units.</p>
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<p>The perimeter of the rectangle is approximately 140.814 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 × (√1049 + 38)</p>
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<p>Perimeter = 2 × (√1049 + 38)</p>
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<p>≈ 2 × (32.407 + 38)</p>
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<p>≈ 2 × (32.407 + 38)</p>
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<p>= 2 × 70.407</p>
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<p>= 2 × 70.407</p>
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<p>= 140.814 units.</p>
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<p>= 140.814 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 1049</h2>
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<h2>FAQ on Square Root of 1049</h2>
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<h3>1.What is √1049 in its simplest form?</h3>
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<h3>1.What is √1049 in its simplest form?</h3>
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<p>Since 1049 is a prime number, √1049 cannot be simplified further.</p>
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<p>Since 1049 is a prime number, √1049 cannot be simplified further.</p>
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<h3>2.Is 1049 a perfect square?</h3>
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<h3>2.Is 1049 a perfect square?</h3>
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<p>No, 1049 is not a perfect square, as it cannot be expressed as the square of an integer.</p>
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<p>No, 1049 is not a perfect square, as it cannot be expressed as the square of an integer.</p>
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<h3>3.Calculate the square of 1049.</h3>
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<h3>3.Calculate the square of 1049.</h3>
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<p>The square of 1049 is obtained by multiplying 1049 by itself: 1049 × 1049 = 1,100,401.</p>
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<p>The square of 1049 is obtained by multiplying 1049 by itself: 1049 × 1049 = 1,100,401.</p>
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<h3>4.Is 1049 a prime number?</h3>
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<h3>4.Is 1049 a prime number?</h3>
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<p>Yes, 1049 is a prime number, as it has no divisors other than 1 and itself.</p>
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<p>Yes, 1049 is a prime number, as it has no divisors other than 1 and itself.</p>
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<h3>5.1049 is divisible by?</h3>
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<h3>5.1049 is divisible by?</h3>
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<p>1049 is not divisible by any integer other than 1 and 1049, confirming it as a prime number.</p>
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<p>1049 is not divisible by any integer other than 1 and 1049, confirming it as a prime number.</p>
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<h2>Important Glossaries for the Square Root of 1049</h2>
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<h2>Important Glossaries for the Square Root of 1049</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 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: 4² = 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 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 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>Prime number:</strong>A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. </li>
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<li><strong>Prime number:</strong>A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. </li>
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<li><strong>Approximation method:</strong>A method used to estimate the square root of non-perfect squares by determining nearby perfect squares. </li>
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<li><strong>Approximation method:</strong>A method used to estimate the square root of non-perfect squares by determining nearby perfect squares. </li>
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<li><strong>Long division method:</strong>A step-by-step process used to find the square root of non-perfect squares, involving repeated division and averaging.</li>
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<li><strong>Long division method:</strong>A step-by-step process used to find the square root of non-perfect squares, involving repeated division and averaging.</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>