Question

Simplify each of the following:

(i) $\sqrt[3]{34}\times \sqrt[3]{316}$

(ii) $\frac{\sqrt[4]{41250}}{\sqrt[4]{42}}$

Answer 1

(i) $\sqrt[3]{34}\times \sqrt[3]{316}=\sqrt[3]{34\times 16}(\because \sqrt{a}\times \sqrt{b}=\sqrt{ab})=\sqrt[3]{364}=\sqrt[3]{34\times 4\times 4}=(4^3{)}^{\frac{1}{3}}=4^{3\times \frac{1}{3}}=4^1=4$

(ii) $\frac{\sqrt[4]{41250}}{\sqrt[4]{42}}=\sqrt[4]{4\frac{1250}{2}}(\because \frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}})=\sqrt[4]{4625}=\sqrt[4]{45\times 5\times 5\times 5}=(5^4{)}^{\frac{1}{4}}=5^{4\times \frac{1}{4}}=5^1=5$