Chapter 4.8, Problem 1LC

Solution

To simplify: The expression $\sqrt{-75}$ using imaginary number $i$ .

  $5\sqrt{3}i$

Given information:

The expression $\sqrt{-75}$ .

Concept used:

Imaginary number: $\sqrt{-1}=i$ .

Calculation:

Use the imaginary number $i$ to simplify the expression as follows:

  $\begin{array}{c}\sqrt{-75}=\sqrt{-1}\sqrt{75}\\ =i\sqrt{75}\\ =\sqrt{75}i\\ =\sqrt{3\cdot 5^2}i\\ =\sqrt{3}\cdot 5i\\ =5\sqrt{3}i\end{array}$

Conclusion:

The simplified expression is $5\sqrt{3}i$ .