Represent $\sqrt{10}$ on the number line.
Let $x$ and $y$ be rational and irrational numbers, respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.
The decimal expansion of the number $\sqrt{2}$ is
Prove that
$\left(\frac{x^{a}}{x^{b}}\right)^{a+b} \times\left(\frac{x^{b}}{x^{c}}\right)^{b+c} \times\left(\frac{x^{c}}{x^{a}}\right)^{c+a}=1$
Rationalise the denominator in each of the following
$\frac{18}{3 \sqrt{2}-2 \sqrt{3}}$