Q. 218 - Intermediate Algebra

Question

Simplify:

$\sqrt{175k^4}-\sqrt{63k^4}$

Step-by-Step Solution

Answer

The value of the given expression is $2k^2\sqrt{7}.$

Step 1. Given Information

The given expression is 

$\sqrt{175k^4}-\sqrt{63k^4}.$

Step 2. Simplify the radicals

Like radicals can be added or subtracted so, 

$$\begin{gathered} \sqrt{175k^4}-\sqrt{63k^4} \\ =\sqrt{25k^4·7}-\sqrt{9k^4·7} \\ =\sqrt{{\left(5k^2\right)}^2}·\sqrt{7}-\sqrt{{\left(3k^2\right)}^2}·\sqrt{7} \\ =\sqrt{7}\left(5k^2-3k^2\right) \\ =2k^2 \sqrt{7} \end{gathered}$$