TEST YOURSELF

Examine whether the following number is rational or irrational.
${\left(\sqrt{2}+2\right)}^2$

Examine whether the following number is rational or irrational.
$\frac{6}{2\sqrt{3}}$

Find one rational and one irrational number between $1.501$ and $1.502.$

Express the following with rational denominator:
$\frac{16}{\sqrt{41}-5}$

Write the following recurring non-terminating decimal in the form $\frac{p}{q}$:  $0.\overline{001}$

Express the following decimals in the $\frac{p}{q}$
$12.3\overline{24}$

Simplify:
${\left(81\right)}^{\frac{3}{4}}$

Simplify: $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$