Q. 224 - Intermediate Algebra

Question

Simplify:

$\sqrt{80a^5}-\sqrt{45a^5}$

Step-by-Step Solution

Answer

The value of the given expression is $a^2\sqrt{5a}$.

Step 1. Given information

The given expression is:

$\sqrt{80a^5}-\sqrt{45a^5}$

Step 2. Simplifying the radicals

Simplifying the radicals, we get:

$$\begin{gathered} \sqrt{80a^5}-\sqrt{45a^5} \\ \sqrt{16a^4·5a}-\sqrt{9a^4·5a} \left[\sqrt{16a^4}=4a^2,\sqrt{9a^4}=3a^2\right] \\ 4a^2\sqrt{5a}-3a^2\sqrt{5a} \end{gathered}$$

Subtracting the like radicals, we get:

$a^2\sqrt{5a}$