Question

Simplify the following :
(i)$4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}\left(ii\right)3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}$

Answer 1

$\left(i\right)4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}=\frac{4\sqrt{28}}{\sqrt[3]{37}}÷3\sqrt{7}=\frac{4\sqrt{28}}{\sqrt[3]{37}\times 3\sqrt{7}}=\frac{4\sqrt{2\times 2\times 7}}{3\times \sqrt{7}\times 7^{\frac{1}{3}}}[\because 28=2\times 2\times 7]=\frac{8}{3\times 7^{\frac{1}{3}}}$

$\left(ii\right)3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}=3\sqrt{3}+2\sqrt{3\times 3\times 3}+\frac{7}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=3\sqrt{3}+6\sqrt{3}+\frac{7\sqrt{3}}{3}=9\sqrt{3}+\frac{7\sqrt{3}}{3}$
$\frac{27\sqrt{3}+7\sqrt{3}}{3}=\frac{34\sqrt{3}}{3}$