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2026-01-01
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<p>Last updated on<strong>December 15, 2025</strong></p>
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<p>Last updated on<strong>December 15, 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 concept extends into complex numbers when dealing with negative numbers. Here, we will discuss the square root of -12.</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 concept extends into complex numbers when dealing with negative numbers. Here, we will discuss the square root of -12.</p>
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<h2>What is the Square Root of -12?</h2>
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<h2>What is the Square Root of -12?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>.</p>
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<p>Since -12 is a<a>negative number</a>, its square root is not a<a>real number</a>. Instead, it is expressed in<a>terms</a>of<a>imaginary numbers</a>.</p>
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<p>Since -12 is a<a>negative number</a>, its square root is not a<a>real number</a>. Instead, it is expressed in<a>terms</a>of<a>imaginary numbers</a>.</p>
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<p>The square root of -12 can be expressed as √(-12) = √(12) × √(-1) = 2√3i, where 'i' is the imaginary unit, defined as √(-1).</p>
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<p>The square root of -12 can be expressed as √(-12) = √(12) × √(-1) = 2√3i, where 'i' is the imaginary unit, defined as √(-1).</p>
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<h2>Finding the Square Root of -12</h2>
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<h2>Finding the Square Root of -12</h2>
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<p>To find the<a>square root</a>of -12, we need to use<a>complex numbers</a>.</p>
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<p>To find the<a>square root</a>of -12, we need to use<a>complex numbers</a>.</p>
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<p>The square root of -12 can be expressed in terms of its real and imaginary components.</p>
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<p>The square root of -12 can be expressed in terms of its real and imaginary components.</p>
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<p>Here, we will explore the method to derive the square root of -12:</p>
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<p>Here, we will explore the method to derive the square root of -12:</p>
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<p>1. Identify the real square root of the positive component, 12.</p>
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<p>1. Identify the real square root of the positive component, 12.</p>
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<p>2. Multiply the result by the imaginary unit '<a>i</a>' to account for the negative sign.</p>
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<p>2. Multiply the result by the imaginary unit '<a>i</a>' to account for the negative sign.</p>
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<h2>Square Root of -12 by Prime Factorization Method</h2>
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<h2>Square Root of -12 by Prime Factorization Method</h2>
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<p>The<a>prime factorization</a>method is used to simplify the positive part of the number before introducing the imaginary unit.</p>
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<p>The<a>prime factorization</a>method is used to simplify the positive part of the number before introducing the imaginary unit.</p>
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<p>Let's explore how this works with -12:</p>
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<p>Let's explore how this works with -12:</p>
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<p><strong>Step 1:</strong>Factorize the positive component, 12, into its prime<a>factors</a>. Breaking it down, we get 2 × 2 × 3 = 2² × 3.</p>
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<p><strong>Step 1:</strong>Factorize the positive component, 12, into its prime<a>factors</a>. Breaking it down, we get 2 × 2 × 3 = 2² × 3.</p>
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<p><strong>Step 2:</strong>Express the square root of 12. √12 = √(2² × 3) = 2√3.</p>
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<p><strong>Step 2:</strong>Express the square root of 12. √12 = √(2² × 3) = 2√3.</p>
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<p><strong>Step 3:</strong>Introduce the imaginary unit for the negative sign. √(-12) = √12 × √(-1) = 2√3 × i = 2√3i.</p>
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<p><strong>Step 3:</strong>Introduce the imaginary unit for the negative sign. √(-12) = √12 × √(-1) = 2√3 × i = 2√3i.</p>
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<h2>Square Root of -12 by Long Division Method</h2>
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<h2>Square Root of -12 by Long Division Method</h2>
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<p>The<a>long division</a>method is typically used for non-<a>perfect square</a>real numbers, but when dealing with negative numbers, we need to use complex number operations.</p>
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<p>The<a>long division</a>method is typically used for non-<a>perfect square</a>real numbers, but when dealing with negative numbers, we need to use complex number operations.</p>
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<p>Therefore, the long division method is not applicable directly for negative numbers like -12.</p>
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<p>Therefore, the long division method is not applicable directly for negative numbers like -12.</p>
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<p>Instead, we use the concept of imaginary numbers as previously discussed.</p>
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<p>Instead, we use the concept of imaginary numbers as previously discussed.</p>
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<h2>Square Root of -12 by Approximation Method</h2>
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<h2>Square Root of -12 by Approximation Method</h2>
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<p>While the approximation method is used for real numbers, for complex numbers such as the square root of -12, we rely on the direct calculation involving imaginary numbers.</p>
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<p>While the approximation method is used for real numbers, for complex numbers such as the square root of -12, we rely on the direct calculation involving imaginary numbers.</p>
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<p>The approximation method is not applicable here since the result involves 'i', the imaginary unit.</p>
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<p>The approximation method is not applicable here since the result involves 'i', the imaginary unit.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -12</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of -12</h2>
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<p>Students often make mistakes when dealing with square roots of negative numbers.</p>
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<p>Students often make mistakes when dealing with square roots of negative numbers.</p>
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<p>Let us look at a few common mistakes and how to avoid them.</p>
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<p>Let us look at a few common mistakes and how to avoid them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>What is the square root of -12 expressed in terms of 'i'?</p>
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<p>What is the square root of -12 expressed in terms of 'i'?</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 of -12 is 2√3i.</p>
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<p>The square root of -12 is 2√3i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Since -12 is a negative number, its square root involves the imaginary unit 'i'.</p>
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<p>Since -12 is a negative number, its square root involves the imaginary unit 'i'.</p>
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<p>Simplifying the positive part, we get √12 = 2√3, and including 'i', we have √(-12) = 2√3i.</p>
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<p>Simplifying the positive part, we get √12 = 2√3, and including 'i', we have √(-12) = 2√3i.</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>If 2√3i is the square root of -12, what is its square?</p>
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<p>If 2√3i is the square root of -12, what is its square?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>-12</p>
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<p>-12</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square, multiply 2√3i by itself:</p>
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<p>To find the square, multiply 2√3i by itself:</p>
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<p>(2√3i)² = (2√3)² × i²</p>
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<p>(2√3i)² = (2√3)² × i²</p>
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<p>= 12 × (-1)</p>
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<p>= 12 × (-1)</p>
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<p>= -12.</p>
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<p>= -12.</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>Express the square root of -12 in terms of the real and imaginary parts.</p>
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<p>Express the square root of -12 in terms of the real and imaginary parts.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Real part: 0, Imaginary part: 2√3</p>
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<p>Real part: 0, Imaginary part: 2√3</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of -12 is completely imaginary, so the real part is 0 and the imaginary part is 2√3.</p>
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<p>The square root of -12 is completely imaginary, so the real part is 0 and the imaginary part is 2√3.</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>How does the square root of -12 relate to the square root of 12?</p>
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<p>How does the square root of -12 relate to the square root of 12?</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 of -12 is the square root of 12 multiplied by 'i'.</p>
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<p>The square root of -12 is the square root of 12 multiplied by 'i'.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of -12 can be expressed as √12 × √(-1)</p>
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<p>The square root of -12 can be expressed as √12 × √(-1)</p>
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<p>= √12 × i</p>
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<p>= √12 × i</p>
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<p>= 2√3i.</p>
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<p>= 2√3i.</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>Is the square root of -12 a real number?</p>
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<p>Is the square root of -12 a real number?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>No, it is a complex number.</p>
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<p>No, it is a complex number.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of a negative number involves the imaginary unit 'i', which makes it a complex number, not a real number.</p>
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<p>The square root of a negative number involves the imaginary unit 'i', which makes it a complex number, not a real number.</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 -12</h2>
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<h2>FAQ on Square Root of -12</h2>
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<h3>1.What is √(-12) in terms of 'i'?</h3>
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<h3>1.What is √(-12) in terms of 'i'?</h3>
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<p>The square root of -12 in terms of 'i' is 2√3i.</p>
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<p>The square root of -12 in terms of 'i' is 2√3i.</p>
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<h3>2.Can the square root of -12 be a real number?</h3>
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<h3>2.Can the square root of -12 be a real number?</h3>
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<p>No, the square root of -12 is not a real number; it is a complex number involving 'i'.</p>
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<p>No, the square root of -12 is not a real number; it is a complex number involving 'i'.</p>
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<h3>3.Why does √(-12) involve 'i'?</h3>
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<h3>3.Why does √(-12) involve 'i'?</h3>
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<p>The square root of a negative number involves 'i' because 'i' is defined as √(-1), which allows us to express square roots of negative numbers.</p>
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<p>The square root of a negative number involves 'i' because 'i' is defined as √(-1), which allows us to express square roots of negative numbers.</p>
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<h3>4.What is the principal square root of -12?</h3>
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<h3>4.What is the principal square root of -12?</h3>
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<p>The principal square root of -12 is 2√3i, focusing on the positive imaginary component.</p>
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<p>The principal square root of -12 is 2√3i, focusing on the positive imaginary component.</p>
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<h3>5.Is the square of 2√3i equal to -12?</h3>
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<h3>5.Is the square of 2√3i equal to -12?</h3>
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<p>Yes, the square of 2√3i equals -12.</p>
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<p>Yes, the square of 2√3i equals -12.</p>
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<h2>Important Glossaries for the Square Root of -12</h2>
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<h2>Important Glossaries for the Square Root of -12</h2>
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<ul><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, it involves imaginary numbers.</li>
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<ul><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, it involves imaginary numbers.</li>
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<li><strong>Imaginary unit 'i':</strong>'i' is defined as the square root of -1 and is used to express square roots of negative numbers.</li>
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<li><strong>Imaginary unit 'i':</strong>'i' is defined as the square root of -1 and is used to express square roots of negative numbers.</li>
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<li><strong>Complex number:</strong>A complex number comprises a real part and an imaginary part, typically expressed as a + bi.</li>
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<li><strong>Complex number:</strong>A complex number comprises a real part and an imaginary part, typically expressed as a + bi.</li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime factors. For example, the prime factorization of 12 is 2² × 3.</li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime factors. For example, the prime factorization of 12 is 2² × 3.</li>
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<li><strong>Principal square root:</strong>In the context of complex numbers, it refers to the positive imaginary component of a negative number's square root.</li>
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<li><strong>Principal square root:</strong>In the context of complex numbers, it refers to the positive imaginary component of a negative number's square root.</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>