Question

Simplify:

(a)$\frac{\sqrt{75q^5}}{\sqrt{108q}}$

(b) $\frac{\sqrt[3]{72b^2}}{\sqrt[3]{9b^5}}$

Short answer

The simplification of $\frac{\sqrt{75q^5}}{\sqrt{108q}}$is $\frac{5q^2}{6}$

The simplification of $\frac{\sqrt[3]{72b^2}}{\sqrt[3]{9b^5}}$ is $\frac{2}{b}$

Step-by-step solution

Part (a) Step 1. Given

An expression $\frac{\sqrt{75q^5}}{\sqrt{108q}}$

To simplify the expression.

Part (a) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt{75q^5}}{\sqrt{108q}}=\sqrt{\frac{75q^5}{108q}}$

Remove the common factor

$=\sqrt{\frac{25q^4}{36}}$

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{75q^5}}{\sqrt{108q}}=\sqrt{\frac{25q^4}{36}}$

$=\frac{5q^2}{6}$

The simplification of the expression is $\frac{5q^2}{6}$

Part (b) Step 1. Given

An expression$\frac{\sqrt[3]{72b^2}}{\sqrt[3]{9b^5}}$

To simplify the expression.

Part (b) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt[3]{72b^2}}{\sqrt[3]{9b^5}}=\sqrt[3]{\frac{72b^2}{9b^5}}$

Remove the common factors.

$=\sqrt[3]{\frac{8}{b^3}}$

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{72b^2}}{\sqrt[3]{9b^5}}=\sqrt[3]{\frac{2^3}{b^3}}$

$=\frac{2}{b}$

The simplification of the expression is $\frac{2}{b}$