Chapter 4.3, Problem 99S

To determine

To calculate: The simplified form of the expression $\sqrt{8}\cdot \sqrt{32}$ .

Answer to Problem 99S

The simplified form of the expression $\sqrt{8}\cdot \sqrt{32}$ is $16$ .

Explanation of Solution

Given information:

The expression $\sqrt{8}\cdot \sqrt{32}$ .

Formula used:

The product of $\sqrt{a}$ and $\sqrt{b}$ is denoted as $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ where a and b are positive integers.

Calculation:

Consider the expression $\sqrt{8}\cdot \sqrt{32}$ .

Recall that product of $\sqrt{a}$ and $\sqrt{b}$ is denoted as $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ where a and b are positive integers.

Apply it,

  $\begin{array}{c}\sqrt{8}\cdot \sqrt{32}=\sqrt{8\left(32\right)}\\ =\sqrt{8\cdot 8\cdot 4}\\ =8\cdot 2\\ =16\end{array}$

Thus, the simplified form of the expression $\sqrt{8}\cdot \sqrt{32}$ is $16$ .