Prove that
$\left(\frac{x^{a}}{x^{b}}\right)^{a+b} \times\left(\frac{x^{b}}{x^{c}}\right)^{b+c} \times\left(\frac{x^{c}}{x^{a}}\right)^{c+a}=1$
Find three different irrational numbers between the rational numbers $\frac{1}{4}$ and $\frac{4}{5}$.
Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$
Rationalise the denominator of the following:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$
Rationalise the denominator of the following: $\frac{\sqrt{40}}{\sqrt{3}}$
The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equal to