Rationalise the denominator of the following:

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

Represent $\sqrt{10}$ on the number line.

Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$

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

If $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}=a+b \sqrt{35},$ find the value of $a$ and $b$.

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.

$\frac{\sqrt{10}-\sqrt{5}}{2}$

The product of any two irrational numbers is