Simplify $\left(4^{\frac{1}{5}}\right)^{3}$.

Is $0.3\overline{7}$ a rational number or an irrational number?

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.
$\frac{1}{\sqrt{3}+\sqrt{2}}$

For each question,select the proper option from four options given,to make the statement true: $4 . \overline{185} = \ldots \ldots$

Insert a rational number and an irrational number between the following: $\sqrt{2}$ and $\sqrt{3}$

Prove that $\frac{x^{a(b-c)}}{x^{b(a-c)}} \div \left(\frac{x^{b}}{x^{a}}\right)^{c} = 1$.