State whether each of the following statements is true or false

$(-5)^{2}=-25$

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.

Fill in the blanks so as to make each of the following statements true (Final answer only)

$(64)^{-\frac{1}{6}}=\ldots \ldots$

Fill in the blanks so as to make each of the following statements true (Final answer only)

$\sqrt{1 \frac{25}{144}}=\ldots \ldots$

Write the following in decimal form and state what kind of decimal expansion each has

$\frac{2}{11}$

In each of the following numbers rationalise the denominator

$\frac{1}{5+2 \sqrt{3}}$