Rationalise the denominator of the following: $\frac{\sqrt{40}}{\sqrt{3}}$

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5} + \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

Rationalise the denominator of the following:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

Which of the following is irrational?

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{1}{\sqrt{3}+\sqrt{2}}$