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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>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 -147.</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 -147.</p>
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<h2>What is the Square Root of -147?</h2>
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<h2>What is the Square Root of -147?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. Since -147 is a<a>negative number</a>, it does not have a real square root because a<a>real number</a>squared is always non-negative. Instead, the square root of -147 is expressed in<a>terms</a>of an<a>imaginary number</a>. In radical form, it is expressed as √-147, which can be written as i√147 in terms of real and imaginary components, where i is the imaginary unit (i² = -1). The approximate value of √147 is 12.124, so the square root of -147 is approximately 12.124i.</p>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. Since -147 is a<a>negative number</a>, it does not have a real square root because a<a>real number</a>squared is always non-negative. Instead, the square root of -147 is expressed in<a>terms</a>of an<a>imaginary number</a>. In radical form, it is expressed as √-147, which can be written as i√147 in terms of real and imaginary components, where i is the imaginary unit (i² = -1). The approximate value of √147 is 12.124, so the square root of -147 is approximately 12.124i.</p>
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<h2>Finding the Square Root of -147</h2>
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<h2>Finding the Square Root of -147</h2>
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<p>To find the<a>square root</a>of a negative number, we use imaginary numbers. Here, we will illustrate how to express the square root of -147 using imaginary numbers:</p>
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<p>To find the<a>square root</a>of a negative number, we use imaginary numbers. Here, we will illustrate how to express the square root of -147 using imaginary numbers:</p>
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<p><strong>Step 1:</strong>Express the negative number in terms of a positive number and the imaginary unit: √-147 = √(147) × √(-1) = √147 × i</p>
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<p><strong>Step 1:</strong>Express the negative number in terms of a positive number and the imaginary unit: √-147 = √(147) × √(-1) = √147 × i</p>
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<p><strong>Step 2:</strong>Calculate the square root of 147, which is approximately 12.124.</p>
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<p><strong>Step 2:</strong>Calculate the square root of 147, which is approximately 12.124.</p>
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<p><strong>Step 3:</strong>Combine the result with the imaginary unit: √-147 = 12.124i</p>
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<p><strong>Step 3:</strong>Combine the result with the imaginary unit: √-147 = 12.124i</p>
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<h2>Square Root of 147 by Prime Factorization Method</h2>
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<h2>Square Root of 147 by Prime Factorization Method</h2>
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<p>To find the square root of 147, we can use the<a>prime factorization</a>method for the positive part of the number:</p>
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<p>To find the square root of 147, we can use the<a>prime factorization</a>method for the positive part of the number:</p>
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<p><strong>Step 1:</strong>The prime factorization of 147 is 3 × 7 × 7 or 3 × 7².</p>
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<p><strong>Step 1:</strong>The prime factorization of 147 is 3 × 7 × 7 or 3 × 7².</p>
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<p><strong>Step 2:</strong>Pair the prime<a>factors</a>: Since we have a pair of 7s, we can take one 7 out of the square root.</p>
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<p><strong>Step 2:</strong>Pair the prime<a>factors</a>: Since we have a pair of 7s, we can take one 7 out of the square root.</p>
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<p><strong>Step 3:</strong>The square root of 147 in simplest form is expressed as √147 = √(3 × 7²) = 7√3.</p>
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<p><strong>Step 3:</strong>The square root of 147 in simplest form is expressed as √147 = √(3 × 7²) = 7√3.</p>
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<p>Thus, the square root of -147 is 7√3i.</p>
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<p>Thus, the square root of -147 is 7√3i.</p>
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<h2>Square Root of -147 by Long Division Method</h2>
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<h2>Square Root of -147 by Long Division Method</h2>
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<p>The<a>long division</a>method is typically used for finding square roots of non-<a>perfect squares</a>. For -147, we are interested in the imaginary square root:</p>
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<p>The<a>long division</a>method is typically used for finding square roots of non-<a>perfect squares</a>. For -147, we are interested in the imaginary square root:</p>
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<p><strong>Step 1:</strong>Consider the positive part, 147, and find its square root using long division, which is approximately 12.124.</p>
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<p><strong>Step 1:</strong>Consider the positive part, 147, and find its square root using long division, which is approximately 12.124.</p>
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<p><strong>Step 2:</strong>Since -147 is negative, the square root is expressed as an imaginary number: √-147 = 12.124i.</p>
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<p><strong>Step 2:</strong>Since -147 is negative, the square root is expressed as an imaginary number: √-147 = 12.124i.</p>
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<h2>Square Root of -147 by Approximation Method</h2>
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<h2>Square Root of -147 by Approximation Method</h2>
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<p>To approximate the square root of -147, we use the square root of 147 and express it in terms of an imaginary number:</p>
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<p>To approximate the square root of -147, we use the square root of 147 and express it in terms of an imaginary number:</p>
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<p><strong>Step 1:</strong>Approximate √147 using the closest perfect squares, 144 and 169. √147 lies between 12 and 13.</p>
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<p><strong>Step 1:</strong>Approximate √147 using the closest perfect squares, 144 and 169. √147 lies between 12 and 13.</p>
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<p><strong>Step 2:</strong>Calculate the<a>decimal</a>approximation: (147 - 144) / (169 - 144) = 3 / 25 = 0.12</p>
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<p><strong>Step 2:</strong>Calculate the<a>decimal</a>approximation: (147 - 144) / (169 - 144) = 3 / 25 = 0.12</p>
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<p><strong>Step 3:</strong>Add the decimal approximation to the lower bound: 12 + 0.12 = 12.12</p>
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<p><strong>Step 3:</strong>Add the decimal approximation to the lower bound: 12 + 0.12 = 12.12</p>
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<p><strong>Step 4:</strong>Therefore, the square root of -147 is approximately 12.12i.</p>
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<p><strong>Step 4:</strong>Therefore, the square root of -147 is approximately 12.12i.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -147</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -147</h2>
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<p>Students often make mistakes when dealing with negative square roots, such as ignoring the imaginary unit or incorrect calculations. Let’s explore some common errors and how to prevent them.</p>
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<p>Students often make mistakes when dealing with negative square roots, such as ignoring the imaginary unit or incorrect calculations. Let’s explore some common errors and how to prevent them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>If the side length of a square is √-98, what is the area of the square in terms of imaginary numbers?</p>
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<p>If the side length of a square is √-98, what is the area of the square in terms of imaginary numbers?</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 -98 square units.</p>
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<p>The area of the square is -98 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 √-98.</p>
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<p>The side length is given as √-98.</p>
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<p>Area = (√-98)² = -98</p>
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<p>Area = (√-98)² = -98</p>
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<p>Therefore, the area of the square is -98 square units.</p>
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<p>Therefore, the area of the square is -98 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 rectangular garden has a length of √-147 meters and a width of 10 meters. What is the perimeter in terms of imaginary numbers?</p>
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<p>A rectangular garden has a length of √-147 meters and a width of 10 meters. What is the perimeter in terms of imaginary numbers?</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 is 20 + 24.248i meters.</p>
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<p>The perimeter is 20 + 24.248i meters.</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 × (√-147 + 10) = 2 × (12.124i + 10) = 20 + 24.248i meters</p>
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<p>Perimeter = 2 × (√-147 + 10) = 2 × (12.124i + 10) = 20 + 24.248i meters</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 3 times the square root of -147.</p>
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<p>Calculate 3 times the square root of -147.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>36.372i</p>
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<p>36.372i</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Find the square root of -147, which is 12.124i.</p>
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<p>Find the square root of -147, which is 12.124i.</p>
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<p>Then multiply by 3: 3 × 12.124i = 36.372i</p>
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<p>Then multiply by 3: 3 × 12.124i = 36.372i</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 is the result of adding √-147 and √-3?</p>
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<p>What is the result of adding √-147 and √-3?</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 result is 14.045i.</p>
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<p>The result is 14.045i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Find the square roots: √-147 = 12.124i √-3 = 1.732i</p>
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<p>Find the square roots: √-147 = 12.124i √-3 = 1.732i</p>
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<p>Add them: 12.124i + 1.732i = 14.045i</p>
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<p>Add them: 12.124i + 1.732i = 14.045i</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>If the hypotenuse of a right triangle is √-147, what is the length in terms of imaginary numbers?</p>
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<p>If the hypotenuse of a right triangle is √-147, what is the length in terms of imaginary numbers?</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 hypotenuse length is 12.124i units.</p>
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<p>The hypotenuse length is 12.124i units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The hypotenuse is given as √-147, which equals 12.124i units.</p>
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<p>The hypotenuse is given as √-147, which equals 12.124i 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 -147</h2>
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<h2>FAQ on Square Root of -147</h2>
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<h3>1.What is √-147 in its simplest form?</h3>
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<h3>1.What is √-147 in its simplest form?</h3>
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<p>The simplest form of √-147 is 7√3i, derived from the prime factorization of 147 as 3 × 7².</p>
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<p>The simplest form of √-147 is 7√3i, derived from the prime factorization of 147 as 3 × 7².</p>
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<h3>2.What is i in the context of square roots?</h3>
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<h3>2.What is i in the context of square roots?</h3>
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<p>The imaginary unit i is defined as √-1, used to represent the square root of negative numbers.</p>
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<p>The imaginary unit i is defined as √-1, used to represent the square root of negative numbers.</p>
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<h3>3.Why does -147 not have a real square root?</h3>
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<h3>3.Why does -147 not have a real square root?</h3>
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<p>Negative numbers do not have real square roots because a real number squared is always non-negative. The square root of a negative number is expressed using the imaginary unit i.</p>
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<p>Negative numbers do not have real square roots because a real number squared is always non-negative. The square root of a negative number is expressed using the imaginary unit i.</p>
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<h3>4.How do you express the square root of a negative number?</h3>
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<h3>4.How do you express the square root of a negative number?</h3>
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<p>The square root of a negative number is expressed using the imaginary unit i. For example, √-147 = √147 × i.</p>
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<p>The square root of a negative number is expressed using the imaginary unit i. For example, √-147 = √147 × i.</p>
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<h3>5.What is the approximate value of √147?</h3>
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<h3>5.What is the approximate value of √147?</h3>
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<p>The approximate value of √147 is 12.124, used to express the square root of -147 as 12.124i.</p>
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<p>The approximate value of √147 is 12.124, used to express the square root of -147 as 12.124i.</p>
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<h2>Important Glossaries for the Square Root of -147</h2>
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<h2>Important Glossaries for the Square Root of -147</h2>
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<ul><li><strong>Imaginary Unit:</strong>Represented by i, it is the square root of -1, used to express square roots of negative numbers.</li>
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<ul><li><strong>Imaginary Unit:</strong>Represented by i, it is the square root of -1, used to express square roots of negative numbers.</li>
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</ul><ul><li><strong>Square Root:</strong>The value that, when multiplied by itself, gives the original number. For negative numbers, it includes the imaginary unit.</li>
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</ul><ul><li><strong>Square Root:</strong>The value that, when multiplied by itself, gives the original number. For negative numbers, it includes the imaginary unit.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>The expression of a number as the product of its prime factors, used for simplifying square roots.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>The expression of a number as the product of its prime factors, used for simplifying square roots.</li>
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</ul><ul><li><strong>Approximation:</strong>A method of finding a near value, applied to non-perfect square roots for estimating decimal values.</li>
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</ul><ul><li><strong>Approximation:</strong>A method of finding a near value, applied to non-perfect square roots for estimating decimal values.</li>
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</ul><ul><li><strong>Real Number:</strong>A value that represents a quantity along a continuous line, excluding imaginary numbers like those involving i.</li>
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</ul><ul><li><strong>Real Number:</strong>A value that represents a quantity along a continuous line, excluding imaginary numbers like those involving i.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>