Which choice is equivalent to the expression below?
\[
\sqrt{-81}
\]
A. 9 i
B. -9
C. \sqrt{9 i}
D. -\sqrt{9}
E. i \sqrt{9}

Answer

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Answer

The equivalent expression to \(\sqrt{-81}\) is \(\boxed{9i}\).

Steps

Step 1 ：The square root of a negative number is an imaginary number.

Step 2 ：The square root of -81 can be written as the square root of 81 times the square root of -1.

Step 3 ：The square root of 81 is 9 and the square root of -1 is represented as 'i' in mathematics.

Step 4 ：Therefore, the square root of -81 is 9i.

Step 5 ：The equivalent expression to \(\sqrt{-81}\) is \(\boxed{9i}\).