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2026-01-01
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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>When a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The concept of square roots extends to complex numbers, where negative numbers also have square roots. Here, we will discuss the square root of -136.</p>
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<p>When a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The concept of square roots extends to complex numbers, where negative numbers also have square roots. Here, we will discuss the square root of -136.</p>
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<h2>What is the Square Root of -136?</h2>
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<h2>What is the Square Root of -136?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. In the case of<a>negative numbers</a>, the square root involves<a>imaginary numbers</a>. The square root of -136 is expressed in the form of √-136, which can be rewritten as √136 ×<a>i</a>, where i is the imaginary unit. The numerical value of √136 is approximately 11.662. Therefore, the square root of -136 is 11.662i, an imaginary number.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. In the case of<a>negative numbers</a>, the square root involves<a>imaginary numbers</a>. The square root of -136 is expressed in the form of √-136, which can be rewritten as √136 ×<a>i</a>, where i is the imaginary unit. The numerical value of √136 is approximately 11.662. Therefore, the square root of -136 is 11.662i, an imaginary number.</p>
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<h2>Finding the Square Root of -136</h2>
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<h2>Finding the Square Root of -136</h2>
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<p>The<a>square root</a>of a negative number involves the imaginary unit 'i'. Common methods to calculate square roots include factoring for<a>perfect squares</a>,<a>long division</a>for non-perfect squares, and approximation. However, for negative numbers, we first compute the square root of the positive counterpart and then multiply by i. Let's examine these methods:</p>
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<p>The<a>square root</a>of a negative number involves the imaginary unit 'i'. Common methods to calculate square roots include factoring for<a>perfect squares</a>,<a>long division</a>for non-perfect squares, and approximation. However, for negative numbers, we first compute the square root of the positive counterpart and then multiply by i. Let's examine these 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 -136 by Prime Factorization Method</h2>
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</ul><h2>Square Root of -136 by Prime Factorization Method</h2>
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<p>Prime factorization involves breaking down a number into its prime components. While -136 is not a perfect square, we can find the<a>prime factorization</a>of 136:</p>
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<p>Prime factorization involves breaking down a number into its prime components. While -136 is not a perfect square, we can find the<a>prime factorization</a>of 136:</p>
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<p><strong>Step 1:</strong>Finding the prime<a>factors</a>of 136 Breaking it down, we get 2 × 2 × 2 × 17: 2³ × 17</p>
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<p><strong>Step 1:</strong>Finding the prime<a>factors</a>of 136 Breaking it down, we get 2 × 2 × 2 × 17: 2³ × 17</p>
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<p><strong>Step 2:</strong>Since -136 is negative, the square root involves 'i'. Thus, √-136 = √136 × i = 2√34 × i</p>
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<p><strong>Step 2:</strong>Since -136 is negative, the square root involves 'i'. Thus, √-136 = √136 × i = 2√34 × i</p>
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<h2>Square Root of -136 by Long Division Method</h2>
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<h2>Square Root of -136 by Long Division Method</h2>
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<p>The long<a>division</a>method is used for non-perfect squares. Let's use this method to find √136, then multiply by i.</p>
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<p>The long<a>division</a>method is used for non-perfect squares. Let's use this method to find √136, then multiply by i.</p>
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<p><strong>Step 1:</strong>Group digits of 136 from right to left: 36 and 1.</p>
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<p><strong>Step 1:</strong>Group digits of 136 from right to left: 36 and 1.</p>
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<p><strong>Step 2:</strong>Find n such that n² ≤ 1. Here, n = 1 as 1 × 1 = 1.</p>
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<p><strong>Step 2:</strong>Find n such that n² ≤ 1. Here, n = 1 as 1 × 1 = 1.</p>
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<p><strong>Step 3:</strong>Subtract 1 from 1 to get 0, then bring down 36.</p>
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<p><strong>Step 3:</strong>Subtract 1 from 1 to get 0, then bring down 36.</p>
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<p><strong>Step 4:</strong>Add 1 to itself to get 2 as the new<a>divisor</a>.</p>
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<p><strong>Step 4:</strong>Add 1 to itself to get 2 as the new<a>divisor</a>.</p>
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<p><strong>Step 5:</strong>Find 2n × n ≤ 36. Let n = 6, then 26 × 6 = 156; adjust to get 216.</p>
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<p><strong>Step 5:</strong>Find 2n × n ≤ 36. Let n = 6, then 26 × 6 = 156; adjust to get 216.</p>
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<p><strong>Step 6:</strong>Subtract 216 from 360 to get 144.</p>
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<p><strong>Step 6:</strong>Subtract 216 from 360 to get 144.</p>
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<p><strong>Step 7:</strong>Add<a>decimal</a>and bring down two zeroes to get 14400.</p>
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<p><strong>Step 7:</strong>Add<a>decimal</a>and bring down two zeroes to get 14400.</p>
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<p><strong>Step 8:</strong>Find the new divisor. Continue the division until reaching a close approximation. Result: √136 ≈ 11.662, so √-136 = 11.662i</p>
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<p><strong>Step 8:</strong>Find the new divisor. Continue the division until reaching a close approximation. Result: √136 ≈ 11.662, so √-136 = 11.662i</p>
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<h2>Square Root of -136 by Approximation Method</h2>
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<h2>Square Root of -136 by Approximation Method</h2>
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<p>The approximation method is used for quick calculations. We find the square root of 136 and multiply by i.</p>
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<p>The approximation method is used for quick calculations. We find the square root of 136 and multiply by i.</p>
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<p><strong>Step 1:</strong>Identify the perfect squares around 136: 121 (11²) and 144 (12²).</p>
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<p><strong>Step 1:</strong>Identify the perfect squares around 136: 121 (11²) and 144 (12²).</p>
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<p><strong>Step 2:</strong>136 is closer to 144, so √136 ≈ 11.662</p>
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<p><strong>Step 2:</strong>136 is closer to 144, so √136 ≈ 11.662</p>
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<p><strong>Step 3:</strong>Therefore, the square root of -136 is 11.662i</p>
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<p><strong>Step 3:</strong>Therefore, the square root of -136 is 11.662i</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -136</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -136</h2>
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<p>Students often make errors when dealing with square roots of negative numbers, especially involving imaginary units. Let's explore common mistakes:</p>
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<p>Students often make errors when dealing with square roots of negative numbers, especially involving imaginary units. Let's explore common mistakes:</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 √-144?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √-144?</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 -144 square units.</p>
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<p>The area of the square is -144 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 √-144.</p>
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<p>The side length is given as √-144.</p>
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<p>Area of the square = side² = (√-144)² = (-12i)² = -144</p>
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<p>Area of the square = side² = (√-144)² = (-12i)² = -144</p>
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<p>Therefore, the area of the square box is -144 square units (considering the negative value as per the context).</p>
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<p>Therefore, the area of the square box is -144 square units (considering the negative value as per the context).</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 -136 square feet is built; if each of the sides is √-136, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring -136 square feet is built; if each of the sides is √-136, 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>-68 square feet</p>
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<p>-68 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Divide the given area by 2 as the building is square-shaped:</p>
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<p>Divide the given area by 2 as the building is square-shaped:</p>
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<p>Dividing -136 by 2 = -68</p>
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<p>Dividing -136 by 2 = -68</p>
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<p>So half of the building measures -68 square feet.</p>
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<p>So half of the building measures -68 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 √-136 × 5.</p>
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<p>Calculate √-136 × 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>58.31i</p>
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<p>58.31i</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 -136, which is 11.662i.</p>
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<p>First, find the square root of -136, which is 11.662i.</p>
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<p>Then multiply 11.662i by 5.</p>
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<p>Then multiply 11.662i by 5.</p>
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<p>So 11.662i × 5 = 58.31i</p>
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<p>So 11.662i × 5 = 58.31i</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 (-136 + 4)?</p>
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<p>What will be the square root of (-136 + 4)?</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 12i</p>
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<p>The square root is 12i</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 (-136 + 4) = -132.</p>
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<p>To find the square root, calculate (-136 + 4) = -132.</p>
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<p>The square root of -132 is √132 × i.</p>
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<p>The square root of -132 is √132 × i.</p>
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<p>Estimate √132 ≈ 11.49, so the result is approximately 11.49i.</p>
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<p>Estimate √132 ≈ 11.49, so the result is approximately 11.49i.</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 √-136 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 √-136 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 2 × (√-136 + 38) = 2 × (11.662i + 38) = 76 + 23.324i units.</p>
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<p>The perimeter of the rectangle is 2 × (√-136 + 38) = 2 × (11.662i + 38) = 76 + 23.324i 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 × (√-136 + 38) = 2 × (11.662i + 38) = 76 + 23.324i units</p>
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<p>Perimeter = 2 × (√-136 + 38) = 2 × (11.662i + 38) = 76 + 23.324i 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 -136</h2>
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<h2>FAQ on Square Root of -136</h2>
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<h3>1.What is √-136 in its simplest form?</h3>
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<h3>1.What is √-136 in its simplest form?</h3>
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<p>The simplest form of √-136 is 11.662i, where i is the imaginary unit, and it represents the square root of -1.</p>
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<p>The simplest form of √-136 is 11.662i, where i is the imaginary unit, and it represents the square root of -1.</p>
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<h3>2.Mention the factors of 136.</h3>
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<h3>2.Mention the factors of 136.</h3>
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<p>Factors of 136 are 1, 2, 4, 8, 17, 34, 68, and 136.</p>
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<p>Factors of 136 are 1, 2, 4, 8, 17, 34, 68, and 136.</p>
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<h3>3.Calculate the square of -136.</h3>
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<h3>3.Calculate the square of -136.</h3>
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<p>The square of -136 is (-136) × (-136) = 18496.</p>
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<p>The square of -136 is (-136) × (-136) = 18496.</p>
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<h3>4.What is an imaginary number?</h3>
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<h3>4.What is an imaginary number?</h3>
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<p>An imaginary number is a<a>complex number</a>that can be written as a<a>real number</a>multiplied by the imaginary unit 'i', where i² = -1.</p>
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<p>An imaginary number is a<a>complex number</a>that can be written as a<a>real number</a>multiplied by the imaginary unit 'i', where i² = -1.</p>
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<h3>5.Is -136 a perfect square?</h3>
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<h3>5.Is -136 a perfect square?</h3>
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<p>No, -136 is not a perfect square because it is negative, and perfect squares are non-negative.</p>
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<p>No, -136 is not a perfect square because it is negative, and perfect squares are non-negative.</p>
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<h2>Important Glossaries for the Square Root of -136</h2>
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<h2>Important Glossaries for the Square Root of -136</h2>
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<ul><li><strong>Imaginary Unit:</strong>The imaginary unit 'i' is defined as the square root of -1, used to express the square roots of negative numbers. </li>
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<ul><li><strong>Imaginary Unit:</strong>The imaginary unit 'i' is defined as the square root of -1, used to express the square roots of negative numbers. </li>
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<li><strong>Complex Number:</strong>A number that comprises a real part and an imaginary part, typically written in the form a + bi. </li>
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<li><strong>Complex Number:</strong>A number that comprises a real part and an imaginary part, typically written in the form a + bi. </li>
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<li><strong>Square Root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, involves the imaginary unit. </li>
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<li><strong>Square Root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, involves the imaginary unit. </li>
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<li><strong>Approximation:</strong>A method of finding an estimated value close to the actual value, used here for finding square roots of non-perfect squares. </li>
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<li><strong>Approximation:</strong>A method of finding an estimated value close to the actual value, used here for finding square roots of non-perfect squares. </li>
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<li><strong>Prime Factorization:</strong>The process of expressing a number as the product of its prime factors, used in simplifying square roots.</li>
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<li><strong>Prime Factorization:</strong>The process of expressing a number as the product of its prime factors, used in simplifying square roots.</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>