QuestionWrite the number as a product of a real number and $i$ . Simplify the radical expression. $\sqrt{-64}$

Studdy Solution

STEP 1

1. We are working with complex numbers, where $i$ is the imaginary unit.
2. The expression $\sqrt{-64}$ involves a negative number under the square root, which indicates the use of imaginary numbers.

STEP 2

1. Express the negative square root in terms of the imaginary unit $i$ .
2. Simplify the radical expression.

STEP 3

Recognize that the square root of a negative number can be expressed using the imaginary unit $i$ , where $i = \sqrt{-1}$ .
$\sqrt{-64} = \sqrt{64} \times \sqrt{-1}$
This can be rewritten as:
$\sqrt{-64} = \sqrt{64} \times i$

STEP 4

Simplify $\sqrt{64}$ :
$\sqrt{64} = 8$
Thus, the expression becomes:
$\sqrt{-64} = 8i$
The simplified expression is:
$\boxed{8i}$

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