Find the value of $64^{\frac{2}{3}}$.

Rationalise the denominator of the following expression:
$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$

Simplify: $\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$

Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}}?$

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

For each question,select the proper option from four options given,to make the statement true: $.............$ is a rational number between $7$ and $8$.