Simplify

$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$

Find five rational numbers between $\frac{2}{7}$ and $\frac{2}{5}$

In each of the following numbers rationalise the denominator

$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$

Simplify the following:

$4 \sqrt{12} \times 7 \sqrt{6}$

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.

$\frac{1}{\sqrt{3}+\sqrt{2}}$