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sqrt(-4)

$\sqrt{-4}$

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Evaluate integers raised to rational exponents

Full solution

Q.

\sqrt{-4}

Recognize Imaginary Unit: We are asked to find the square root of $-4$ , which is written as $\sqrt{-4}$ . To solve this, we need to recognize that the square root of a negative number involves the imaginary unit 'i', where $i^2 = -1$ .
Express as Product: Since we cannot have a real number as the square root of a negative number, we express $-4$ as $-1 \times 4$ to separate the negative part. $\newline$ $\sqrt{-4} = \sqrt{-1 \times 4}$
Take Square Roots Separately: Now we can take the square root of each factor separately. $\newline$ $\sqrt{-1 \times 4} = \sqrt{-1} \times \sqrt{4}$
Evaluate Square Roots: We know that $\sqrt{-1}$ is the imaginary unit ' $i$ ' and $\sqrt{4}$ is $2$ . So, $\sqrt{-1} \times \sqrt{4} = i \times 2$
Final Answer: Multiplying the imaginary unit ' $i$ ' by $2$ gives us the final answer. $\newline$ $i \times 2 = 2i$

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