Problem

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}

Solution

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 \(\boxed{9i}\).

From Solvely APP
Source: https://solvelyapp.com/problems/7954/

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