Chapter 10.2, Problem 18P

Simplify each product.

$\sqrt{2n^2}\cdot \sqrt{30n}$

To determine

To simplify the product.

Answer to Problem 18P

The simplified product is $2n\sqrt{15n}$ .

Explanation of Solution

Given information:

The given expression is:

  $\sqrt{2n^2}\cdot \sqrt{30n}$

Calculation :

The expression can be simplified by:

$\begin{array}{l}\sqrt{2n^2}\cdot \sqrt{30n}\\ =\sqrt{2n^2\times 30n}\\ =\sqrt{2\times 2\times 3\times 5\times n^2\times n}\left[\text{Write the factors}\right]\\ =2n\sqrt{15n}\end{array}$

Hence, the simplified product is $2n\sqrt{15n}$ .