Add $: 0 . \overline{35}+0 . \overline{28}$

Insert a rational number and an irrational number between the following:

$\sqrt{2}$ and $\sqrt{3}$

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

prove that

$\frac{x^{a(b-c)}}{x^{b(a-c)}} \div\left(\frac{x^{b}}{x^{a}}\right)^{c}=1$

Find three different irrational numbers between the irrational numbers $\sqrt{2}$ and $\sqrt{5}$.

Classify the following numbers as rational or irrational with justification:

$(i)$ $-\sqrt{0.4}$

$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$