Question

score: 0 of 5 points. simplify each expression in exact form and rewrite complex expressions in terms of i. a. $sqrt{-27}=3sqrt{3}i$ b. $sqrt{-8}=2sqrt{2}i$ incorrect! we kindly recommend reviewing the expressing square roots of negative numbers as multiples of i or alternatively, you may engage in a discussion with mathgpt for a comprehensive explanation.

Explanation:

Step1: Recall the property of square - root of negative numbers

We know that $\sqrt{-a}=\sqrt{a}\times\sqrt{- 1}$, and $\sqrt{-1}=i$.

Step2: Simplify $\sqrt{-27}$

First, factorize $27$ as $27 = 9\times3$. Then $\sqrt{-27}=\sqrt{27}\times\sqrt{-1}=\sqrt{9\times3}\times i = 3\sqrt{3}i$.

Step3: Simplify $\sqrt{-8}$

Factorize $8$ as $8 = 4\times2$. Then $\sqrt{-8}=\sqrt{8}\times\sqrt{-1}=\sqrt{4\times2}\times i=2\sqrt{2}i$.

Answer:

a. $\sqrt{-27}=3\sqrt{3}i$
b. $\sqrt{-8}=2\sqrt{2}i$