$\sqrt{10} \times \sqrt{15}$ is equal to

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.

Visualise $-4.126$ on the number line, using successive magnification.

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:

$(i)$ $x^{2}=5$

$(ii)$ $\quad y^{2}=9$

$(iii)$ $z^{2}=.04$

$(iv)$ $u^{2}=\frac{17}{4}$

Rationalise the denominator of the following:

$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$

$\frac{1}{\sqrt{3}+\sqrt{2}}$