Question

Solve: $4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}$

Answer 1

$4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}$

$=\left[\frac{\left(4\sqrt{28}\right)}{\left(3\sqrt{7}\right)}\right]÷7^{\frac{1}{3}}$

$=\left[\frac{\left(4\sqrt{4\times 7}\right)}{\left(3\sqrt{7}\right)}\right]÷7^{\frac{1}{3}}$

$=\left[\frac{4\times 2\sqrt{7}}{3\sqrt{7}}\right]÷7^{\frac{1}{3}}$

$=\frac{8}{3}÷7^{\frac{1}{3}}$

$=\frac{8}{(3\times 7^{\frac{1}{3}})}$

$=\frac{8}{(3\times \sqrt[3]{37})}$