QuestionAugust 24, 2025

Simplify the following square root expression. (sqrt (-128))(sqrt (-2))

Simplify the following square root expression. (sqrt (-128))(sqrt (-2))
Simplify the following square root expression. (sqrt (-128))(sqrt (-2))

Solution
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Answer

-16 Explanation 1. Simplify the square roots Use i = \sqrt{-1} to express \sqrt{-128} = \sqrt{128} \cdot i and \sqrt{-2} = \sqrt{2} \cdot i. 2. Multiply the expressions (\sqrt{128} \cdot i)(\sqrt{2} \cdot i) = \sqrt{128} \cdot \sqrt{2} \cdot i^2. 3. Simplify further \sqrt{128} \cdot \sqrt{2} = \sqrt{256} = 16, and i^2 = -1. 4. Calculate the final result 16 \cdot (-1) = -16.

Explanation

1. Simplify the square roots<br /> Use $i = \sqrt{-1}$ to express $\sqrt{-128} = \sqrt{128} \cdot i$ and $\sqrt{-2} = \sqrt{2} \cdot i$.<br />2. Multiply the expressions<br /> $(\sqrt{128} \cdot i)(\sqrt{2} \cdot i) = \sqrt{128} \cdot \sqrt{2} \cdot i^2$.<br />3. Simplify further<br /> $\sqrt{128} \cdot \sqrt{2} = \sqrt{256} = 16$, and $i^2 = -1$.<br />4. Calculate the final result<br /> $16 \cdot (-1) = -16$.
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