Q. 227 - Intermediate Algebra

Question

Simplify:

$8\sqrt[3]{64q^6}-3\sqrt[3]{125q^6}$

Step-by-Step Solution

Answer

The value of the given expression is $17q^2$.

Step 1. Given information

The given expression is $8\sqrt[3]{64q^6}-3\sqrt[3]{125q^6}$

Step 2. Simplifying the expression

Simplifying the radicals, we get:

$$\begin{gathered} 8\sqrt[3]{64q^6}-3\sqrt[3]{125q^6} \\ 8\sqrt[3]{{\left(4q^2\right)}^3}-3\sqrt[3]{{\left(5q^2\right)}^3} \\ 8·4q^2-3·5q^2 [\sqrt[3]{64q^2}=4q^2,\sqrt[3]{125q^6}=5q^2] \\ 32q^2-15q^2 \end{gathered}$$

Subtracting the like radicals, we get:

$$\begin{gathered} 32q^2-15q^2 \\ 17q^2 \end{gathered}$$