Q. 8.22 - Intermediate Algebra

Question

Simplify: $\left(a\right) \sqrt[3]{125q^9} \left(b\right) \sqrt[5]{243q^{25}}$

Step-by-Step Solution

Answer

The solution of (a) and (b) are $5q^3 and 3q^5$ respectively.

Part (a) Step 1. Given information

The root: $\sqrt[3]{125q^9}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{125q^9} \\ =\sqrt[3]{{\left(5q^3\right)}^3} rewrite 125q^9 as {\left(5q^3\right)}^3 \\ =5q^3 \end{gathered}$$

Therefore, the solution is $5q^3$

Part (b) Step 1. Given information

The root: $\sqrt[5]{243q^{25}}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{243q^{25}} \\ =\sqrt[5]{{\left(3q^5\right)}^5} rewrite 243q^{25} as {\left(3q^5\right)}^5 \\ =3q^5 \end{gathered}$$

Therefore, the solution is$3q^5$