Question

Simplify:

(a)$\frac{\sqrt{50s^3}}{\sqrt{128s}}$

(b)$\frac{\sqrt[3]{56a}}{\sqrt[3]{7a^4}}$

Short answer

The simplification of $\frac{\sqrt{50s^3}}{\sqrt{128s}}$is $\frac{5s}{8}$

The simplification of $\frac{\sqrt[3]{56a}}{\sqrt[3]{7a^4}}$ is $\frac{2}{a}$

Step-by-step solution

Part (a) Step 1. Given

An expression $\frac{\sqrt{50s^3}}{\sqrt{128s}}$

To simplify the expression.

Part (a) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt{50s^3}}{\sqrt{128s}}=\sqrt{\frac{50s^3}{128s}}$

Remove the common factors.

$=\sqrt{\frac{25s^2}{64}}$

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{50s^3}}{\sqrt{128s}}=\sqrt{\frac{25s^2}{64}}$

$=\frac{5s}{8}$

The simplification of given expression is $\frac{5s}{8}$

Part (b) Step 1. Given

An expression$\frac{\sqrt[3]{56a}}{\sqrt[3]{7a^4}}$

To simplify the expression.

Part (b) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt[3]{56a}}{\sqrt[3]{7a^4}}=\sqrt[3]{\frac{56a}{7a^4}}$

Remove the common factors.

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

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{56a}}{\sqrt[3]{7a^4}}=\sqrt[3]{\frac{8}{a^3}}$

$=\sqrt[3]{\frac{2^3}{a^3}}$

$=\frac{2}{a}$

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