Add $4 \sqrt{3}+2 \sqrt{5}$ and $6 \sqrt{3}-4 \sqrt{5}$.
If $125^{x}=\frac{25}{5^{x}},$ then find the value of $x$.
State whether the following statements are true or false? Justify your answer.
$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.
$(ii)$ There are infinitely many integers between any two integers.
Is $0.3 \overline{7}$ a rational number or an irrational number?
Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.
$\frac{4}{\sqrt{3}}$