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.

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

Simplify:

$(\frac{1}{27})^{\frac{-2}{3}}$

Insert a rational number and an irrational number between the following:

$\sqrt{2}$ and $\sqrt{3}$

State whether each of the following statements is true or false

$\sqrt{3} \times \sqrt{5}=\sqrt{8}$

Rationalise the denominator in each of the following

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

Write the following in decimal form and state what kind of decimal expansion each has

$\frac{121}{400}$