Chapter 16.7, Problem 4MRE

To determine

To find: $\sqrt{-2}.\sqrt{-8}=?$

Answer to Problem 4MRE

  $-4$

Explanation of Solution

Given: $\sqrt{-2}.\sqrt{-8}$

Concept Used: $i=\sqrt{-1}$

  $i^2=-1$

  $\sqrt{-2}$ can be written as $\sqrt{-1}.\sqrt{2}$ or $i.\sqrt{2}$

Similarly,

  $\sqrt{-8}$ can be written as $\sqrt{-1}.\sqrt{8}$ or $i.\sqrt{8}$

Now, solving the given expression by using the above:

  $\begin{array}{l}\sqrt{-2}.\sqrt{-8}\\ \Rightarrow i.\sqrt{2}.i.\sqrt{8}\\ \Rightarrow i^2.\sqrt{2}.\sqrt{8}\\ \Rightarrow -1.\sqrt{16}\\ \Rightarrow -4\end{array}$