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Math  /  Numbers & Operations

QuestionFind the square root of the number. −24\sqrt{-24}
The square root is □\square

Studdy Solution

STEP 1

1. We are dealing with the square root of a negative number.
2. The solution will involve complex numbers since the square root of a negative number is not real.

STEP 2

1. Identify the components of the square root.
2. Express the square root in terms of imaginary numbers.
3. Simplify the expression.

STEP 3

Recognize that −24\sqrt{-24} involves the square root of a negative number, which can be expressed in terms of imaginary numbers.

STEP 4

Express −24\sqrt{-24} using the imaginary unit ii, where i=−1i = \sqrt{-1}.
−24=24⋅−1=24⋅i\sqrt{-24} = \sqrt{24} \cdot \sqrt{-1} = \sqrt{24} \cdot i

STEP 5

Simplify 24\sqrt{24} by factoring out the largest perfect square.
24=4×6=4⋅6=26\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}

STEP 6

Combine the expressions to write the final solution.
−24=26⋅i=2i6\sqrt{-24} = 2\sqrt{6} \cdot i = 2i\sqrt{6}
The square root is:
2i6\boxed{2i\sqrt{6}}

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