Rationalisation

Write the rationalizing factor of : $\frac{1}{\mathrm{x}+\sqrt{\mathrm{y}}}$

Write the rationalizing factor of : $5-2\sqrt{3}$

What denominator do we get after rationalising the denominator of $\frac{5}{3\sqrt{3}+2\sqrt{2}}?$

If $\mathrm{x}=2+\sqrt{3}$, then find the value of ${\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}$.

If $\mathrm{a}-\mathrm{b}\sqrt{3}=\frac{2-\sqrt{3}}{2+\sqrt{3}}$, then find the value of $\mathrm{\text{'}}\mathrm{a}\mathrm{\text{'}}$ and $\mathrm{\text{'}}\mathrm{b}\mathrm{\text{'}}$.

Rationalize: $\frac{1}{7+3\sqrt{2}}$

Rationalize: $\frac{5}{\sqrt{3}-\sqrt{5}}$

Rationalize: $\frac{1}{2-\sqrt{3}}$

Rationalize: $\frac{1}{\sqrt{2}}$