Rationalisation

Evaluate $\frac{\sqrt{\left(x^2-1\right)}}{x-\sqrt{x^2-1}}$ when $2x=\sqrt{a}+\frac{1}{\sqrt{a}}$

Find the value of $\sqrt{\frac{6+2\sqrt{3}}{33-19\sqrt{3}}}$

If $a=\frac{1}{2-\sqrt{3}}, b=\frac{1}{2+\sqrt{3}},$ then  find the value of $7a^2+11ab-7b^2$

Find the square root of $1+{\left(1-a^2\right)}^{-\frac{1}{2}}$

Express with rational denominator $\frac{\sqrt[6]{27}}{3-\sqrt[6]{9}}$ 

Express with rational denominator $\frac{\sqrt{8}+\sqrt[3]{4}}{\sqrt{8}-\sqrt[3]{4}}$

Express with rational denominator  $\frac{\sqrt[3]{3}}{\sqrt{3}+\sqrt[6]{9}}$

Express with rational denominator $\frac{\sqrt{2}-\sqrt[3]{3}}{\sqrt[3]{3}+\sqrt{2}}$

Express $\left(\frac{\sqrt[6]{9}-\sqrt[6]{8}}{\sqrt[6]{9}+\sqrt[6]{8}}\right)$ with rational denominator.

Express with rational denominator $\left(\frac{\sqrt[3]{3}-1}{\sqrt[3]{3}+1}\right)$

Find the factor which will rationalise $\sqrt[3]{5}-\sqrt[4]{3}$.

Find the factor which will rationalise $2+\sqrt[4]{7}$.

Find the factor which will rationalise  $\sqrt[3]{3}-1$.

Find the factor which will rationalise $a^{\frac{1}{6}}+b^{\frac{1}{4}}$

Find the factor which will rationalise  $\sqrt[6]{5}+\sqrt[3]{2}$.

Find a factor which will rationalise

$\sqrt[3]{3}-\sqrt{2}$

Express as an equivalent fraction with rational denominator, $\frac{\left(\sqrt{3}+\sqrt{5}\right)(\sqrt{5}+\sqrt{2})}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$

Express as an equivalent fraction with rational denominator, $\frac{\sqrt{10}+\sqrt{5}-\sqrt{3}}{\sqrt{3}+\sqrt{10}-\sqrt{5}}$

Express as an equivalent fraction with rational denominator,

$\frac{2\sqrt{a+1}}{\sqrt{a-1}-\sqrt{2a}+\sqrt{a+1}}$

Express as an equivalent fraction with rational denominator,

$\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{a+b}}$