Chapter 10.2, Problem 15P

Simplify each product.

$2\sqrt{3}\cdot \sqrt{96}$

To determine

To simplify the product.

Answer to Problem 15P

The simplified product is $24\sqrt{2}$ .

Explanation of Solution

Given information:

The given expression is:

  $2\sqrt{3}\cdot \sqrt{96}$

Calculation :

The expression can be simplified by:

$\begin{array}{l}2\sqrt{3}\cdot \sqrt{96}\\ =2\sqrt{3\times 96}\\ =2\sqrt{3\times 2\times 2\times 2\times 2\times 2\times 3}\left[\text{Write the factors}\right]\\ =2\cdot 2\cdot 2\cdot 3\sqrt{2}\\ =24\sqrt{2}\end{array}$

Hence, the simplified product is $24\sqrt{2}$ .