Chapter 10.2, Problem 16P

Simplify each product.

$-4\sqrt{7}\cdot \sqrt{42}$

To determine

To simplify the product.

Answer to Problem 16P

The simplified product is $-28\sqrt{6}$ .

Explanation of Solution

Given information:

The given expression is:

  $-4\sqrt{7}\cdot \sqrt{42}$

Calculation :

The expression can be simplified by:

$\begin{array}{l}-4\sqrt{7}\cdot \sqrt{42}\\ =-4\sqrt{7\times 42}\\ =-4\sqrt{7\times 2\times 3\times 7}\left[\text{Write the factors}\right]\\ =-4\cdot 7\sqrt{2\times 3}\\ =-28\sqrt{6}\end{array}$

Hence, the simplified product is $-28\sqrt{6}$ .