Simplify:
${{(625)^{-\frac{1}{2}}}^{-\frac{1}{4}}}^{2}$
If $\frac{5+3 \sqrt{3}}{7+4 \sqrt{3}}=a+b \sqrt{3},$ find the value of $a$ and $b$
Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$
Insert a rational number and an irrational number between the following:
$\frac{1}{3}$ and $\frac{1}{2}$
Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Simplify:
$\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$