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2026-01-01
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2026-02-21
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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 itself, the result is a square. The inverse of a square is a square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7.05.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7.05.</p>
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<h2>What is the Square Root of 7.05?</h2>
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<h2>What is the Square Root of 7.05?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 7.05 is not a<a>perfect square</a>. The square root of 7.05 is expressed in both radical and exponential forms. In radical form, it is expressed as √7.05, whereas in<a>exponential form</a>it is (7.05)^(1/2). √7.05 ≈ 2.655, 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>. 7.05 is not a<a>perfect square</a>. The square root of 7.05 is expressed in both radical and exponential forms. In radical form, it is expressed as √7.05, whereas in<a>exponential form</a>it is (7.05)^(1/2). √7.05 ≈ 2.655, 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 7.05</h2>
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<h2>Finding the Square Root of 7.05</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:</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:</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 7.05 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 7.05 by Prime Factorization Method</h2>
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<p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. However, since 7.05 is not a perfect square, it cannot be exactly broken down into pairs of prime factors to find its<a>square root</a>using this method. Therefore, calculating √7.05 using prime factorization is not feasible.</p>
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<p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. However, since 7.05 is not a perfect square, it cannot be exactly broken down into pairs of prime factors to find its<a>square root</a>using this method. Therefore, calculating √7.05 using prime factorization is not feasible.</p>
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<h2>Square Root of 7.05 by Long Division Method</h2>
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<h2>Square Root of 7.05 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, group the numbers from right to left. In the case of 7.05, we treat it as 705.</p>
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<p><strong>Step 1:</strong>To begin, group the numbers from right to left. In the case of 7.05, we treat it as 705.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 7. The closest such number is 2, because 2 × 2 = 4.</p>
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<p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 7. The closest such number is 2, because 2 × 2 = 4.</p>
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<p><strong>Step 3:</strong>Subtract 4 from 7, getting a<a>remainder</a>of 3. Bring down the next pair of digits (05) to get 305.</p>
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<p><strong>Step 3:</strong>Subtract 4 from 7, getting a<a>remainder</a>of 3. Bring down the next pair of digits (05) to get 305.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(2) to get 4. Now, find a number n such that 4n × n ≤ 305. The closest number is 6, because 46 × 6 = 276.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(2) to get 4. Now, find a number n such that 4n × n ≤ 305. The closest number is 6, because 46 × 6 = 276.</p>
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<p><strong>Step 5:</strong>Subtract 276 from 305, the remainder is 29.</p>
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<p><strong>Step 5:</strong>Subtract 276 from 305, the remainder is 29.</p>
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<p><strong>Step 6:</strong>Add a<a>decimal</a>point and bring down 00 to get 2900.</p>
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<p><strong>Step 6:</strong>Add a<a>decimal</a>point and bring down 00 to get 2900.</p>
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<p><strong>Step 7:</strong>The new divisor is 52. Find a number n such that 52n × n ≤ 2900. The closest number is 5, because 525 × 5 = 2625.</p>
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<p><strong>Step 7:</strong>The new divisor is 52. Find a number n such that 52n × n ≤ 2900. The closest number is 5, because 525 × 5 = 2625.</p>
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<p><strong>Step 8:</strong>Subtract 2625 from 2900, getting a remainder of 275.</p>
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<p><strong>Step 8:</strong>Subtract 2625 from 2900, getting a remainder of 275.</p>
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<p><strong>Step 9:</strong>The<a>quotient</a>so far is 2.65. Continue these steps until you get the desired precision.</p>
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<p><strong>Step 9:</strong>The<a>quotient</a>so far is 2.65. Continue these steps until you get the desired precision.</p>
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<h2>Square Root of 7.05 by Approximation Method</h2>
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<h2>Square Root of 7.05 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 7.05 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 7.05 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 7.05.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 7.05.</p>
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<p>The closest perfect squares are 4 (√4 = 2) and 9 (√9 = 3).</p>
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<p>The closest perfect squares are 4 (√4 = 2) and 9 (√9 = 3).</p>
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<p><strong>Step 2:</strong>7.05 is closer to 4 than to 9. Its square root will be closer to 2.</p>
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<p><strong>Step 2:</strong>7.05 is closer to 4 than to 9. Its square root will be closer to 2.</p>
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<p><strong>Step 3:</strong>Use interpolation or<a>estimation</a>to refine the approximation: (7.05 - 4) / (9 - 4) ≈ 0.61.</p>
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<p><strong>Step 3:</strong>Use interpolation or<a>estimation</a>to refine the approximation: (7.05 - 4) / (9 - 4) ≈ 0.61.</p>
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<p><strong>Step 4:</strong>The approximation of √7.05 ≈ 2 + 0.61 = 2.61. Continue refining the approximation for greater<a>accuracy</a>.</p>
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<p><strong>Step 4:</strong>The approximation of √7.05 ≈ 2 + 0.61 = 2.61. Continue refining the approximation for greater<a>accuracy</a>.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7.05</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7.05</h2>
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<p>Students often make mistakes while finding square roots, such as ignoring the negative square root or skipping steps in long division methods. Let us look at some common mistakes in detail.</p>
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<p>Students often make mistakes while finding square roots, such as ignoring the negative square root or skipping steps in long division methods. Let us look at some common mistakes in detail.</p>
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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 √7.05?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √7.05?</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 7.05 square units.</p>
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<p>The area of the square is approximately 7.05 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 a square is side².</p>
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<p>The area of a square is side².</p>
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<p>The side length is given as √7.05.</p>
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<p>The side length is given as √7.05.</p>
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<p>Area of the square = side² = (√7.05)² = 7.05.</p>
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<p>Area of the square = side² = (√7.05)² = 7.05.</p>
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<p>Therefore, the area of the square box is approximately 7.05 square units.</p>
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<p>Therefore, the area of the square box is approximately 7.05 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 7.05 square feet is built; if each of the sides is √7.05, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 7.05 square feet is built; if each of the sides is √7.05, 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>3.525 square feet</p>
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<p>3.525 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 7.05 by 2 = 3.525.</p>
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<p>Dividing 7.05 by 2 = 3.525.</p>
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<p>So, half of the building measures 3.525 square feet.</p>
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<p>So, half of the building measures 3.525 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 √7.05 × 5.</p>
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<p>Calculate √7.05 × 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 13.275</p>
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<p>Approximately 13.275</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 7.05, which is approximately 2.655.</p>
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<p>First, find the square root of 7.05, which is approximately 2.655.</p>
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<p>Multiply 2.655 by 5.</p>
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<p>Multiply 2.655 by 5.</p>
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<p>So, 2.655 × 5 ≈ 13.275.</p>
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<p>So, 2.655 × 5 ≈ 13.275.</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 (7 + 0.05)?</p>
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<p>What will be the square root of (7 + 0.05)?</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 2.655</p>
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<p>Approximately 2.655</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 (7 + 0.05). 7 + 0.05 = 7.05, and then √7.05 ≈ 2.655.</p>
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<p>To find the square root, calculate the sum of (7 + 0.05). 7 + 0.05 = 7.05, and then √7.05 ≈ 2.655.</p>
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<p>Therefore, the square root of (7 + 0.05) is approximately ±2.655.</p>
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<p>Therefore, the square root of (7 + 0.05) is approximately ±2.655.</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 a rectangle if its length ‘l’ is √7.05 units and the width ‘w’ is 4 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √7.05 units and the width ‘w’ is 4 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 13.31 units.</p>
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<p>The perimeter of the rectangle is approximately 13.31 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width).</p>
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<p>Perimeter of a rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√7.05 + 4) = 2 × (2.655 + 4) = 2 × 6.655 = 13.31 units.</p>
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<p>Perimeter = 2 × (√7.05 + 4) = 2 × (2.655 + 4) = 2 × 6.655 = 13.31 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 7.05</h2>
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<h2>FAQ on Square Root of 7.05</h2>
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<h3>1.What is √7.05 in its simplest form?</h3>
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<h3>1.What is √7.05 in its simplest form?</h3>
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<p>The simplest form of √7.05 is in its decimal approximation, which is approximately 2.655, as it cannot be simplified further into a rational form.</p>
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<p>The simplest form of √7.05 is in its decimal approximation, which is approximately 2.655, as it cannot be simplified further into a rational form.</p>
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<h3>2.Mention the factors of 7.05.</h3>
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<h3>2.Mention the factors of 7.05.</h3>
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<p>The factors of 7.05 in its decimal form are not integers, but it can be expressed as the product of its prime factors in fractional form: 7.05 = 141/20 = 3^1 × 47/2^2 × 5.</p>
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<p>The factors of 7.05 in its decimal form are not integers, but it can be expressed as the product of its prime factors in fractional form: 7.05 = 141/20 = 3^1 × 47/2^2 × 5.</p>
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<h3>3.Calculate the square of 7.05.</h3>
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<h3>3.Calculate the square of 7.05.</h3>
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<p>We get the square of 7.05 by multiplying the number by itself: 7.05 × 7.05 = 49.7025.</p>
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<p>We get the square of 7.05 by multiplying the number by itself: 7.05 × 7.05 = 49.7025.</p>
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<h3>4.Is 7.05 a prime number?</h3>
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<h3>4.Is 7.05 a prime number?</h3>
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<h3>5.7.05 is divisible by?</h3>
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<h3>5.7.05 is divisible by?</h3>
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<p>7.05 is divisible by 1 and itself. In fractional<a>terms</a>, it can be divided by 1, 3, 47, and 141.</p>
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<p>7.05 is divisible by 1 and itself. In fractional<a>terms</a>, it can be divided by 1, 3, 47, and 141.</p>
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<h2>Important Glossaries for the Square Root of 7.05</h2>
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<h2>Important Glossaries for the Square Root of 7.05</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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</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, but the positive square root is more commonly used in real-world applications, known as the principal square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is more commonly used in real-world applications, known as the principal square root.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find square roots of non-perfect squares by dividing the number into groups and solving step-by-step.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find square roots of non-perfect squares by dividing the number into groups and solving step-by-step.</li>
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</ul><ul><li><strong>Approximation method:</strong>A technique for estimating the square root of a number by comparing it with nearby perfect squares and refining the result through interpolation.</li>
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</ul><ul><li><strong>Approximation method:</strong>A technique for estimating the square root of a number by comparing it with nearby perfect squares and refining the result through interpolation.</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>