Insert a rational number and an irrational number between the following:
$6.375289$ and $6.375738$

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{2}{11}$

Simplify: $\frac{11^{\frac{1}{3}}}{11^{\frac{1}{5}}}$

State whether the following statements are true or false. Justify your answer.
$(i)$ The square of an irrational number is always rational.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.

Arrange the following numbers in ascending order: $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$