Chapter 10.2, Problem 14P

Simplify each product.

$\sqrt{5}\cdot \sqrt{70}$

To determine

To simplify the product.

Answer to Problem 14P

The simplified product is $5\sqrt{14}$ .

Explanation of Solution

Given information:

The given expression is:

  $\sqrt{5}\cdot \sqrt{70}$

Calculation :

The expression can be simplified by:

$\begin{array}{l}\sqrt{5}\cdot \sqrt{70}\\ =\sqrt{5\times 70}\\ =\sqrt{5\times 2\times 5\times 7}\left[\text{Write the factors}\right]\\ =5\sqrt{2\times 7}\\ =5\sqrt{14}\end{array}$

Hence, the simplified product is $5\sqrt{14}$ .