Question

Simplify the following:

${\displaystyle 4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{7}}$

Answer 1

${\displaystyle 4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{7}=(4\sqrt{4\times 7}÷3\sqrt{7})÷\sqrt[3]{7}}$

= ${\displaystyle \left(\frac{8\sqrt{7}}{3\sqrt{7}}\right)÷{\left(7\right)}^{\frac{1}{3}}}$   ...${\displaystyle [\because \sqrt[n]{a}=a^{\frac{1}{n}}]}$

= ${\displaystyle \frac{8}{3}÷7^{\frac{1}{3}}}$

= ${\displaystyle \frac{8}{3\sqrt[3]{7}}}$