Question:
Simplify each of the following:
(i) $\sqrt[3]{4} \times \sqrt[3]{16}$
(ii) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$
Solution:
(i) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$
(Note: $\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$ )
$=\sqrt[3]{4 \times 16}$
$=\sqrt[3]{64}$
$=\sqrt[3]{4^{3}}$
$=\left(4^{3}\right)^{1 / 3}$
$=4^{(3 \times 1 / 3)}$
$=4^{1}$
$=4$
(ii) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$
$\left(\right.$ Note: $\left.\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}\right)$
$=\sqrt[4]{\frac{1250}{2}}$
$=\sqrt[4]{\frac{2 \times 625}{2}}$
$=\sqrt[4]{625}$
$=\sqrt[4]{15^{4}}$
$=15^{(4 \times 1 / 4)}$
$=15$