Chapter 7.1, Problem 1MRE

To determine

To Simplify:

  $\sqrt{-50}$

Answer to Problem 1MRE

  $5i\sqrt{2}$

Explanation of Solution

Given:

The expression is :

  $\sqrt{-50}$

Calculation:

Given:

  $\begin{array}{l}\sqrt{-50}\\ =\sqrt{-1}\cdot \sqrt{5^2\cdot 2}\mathrm{................}[\text{factor in squares]}\\ =5i\sqrt{2}\mathrm{...........................}[\sqrt{-1}=i]\end{array}$

Since 2 does not have any perfect square root, it is in the simplest form.

So,

  $5i\sqrt{2}$ is the solution.