Question

Rationalise the surd $(5\sqrt{x}-3\sqrt{y})$

Answer 1

$(5\sqrt{x}-3\sqrt{y})(5\sqrt{x}+3\sqrt{y})$
$=(5\sqrt{x}{)}^2-(3\sqrt{y}{)}^2\{\because (a-b\left)\right(a+b)=a^2-b^2\}$
$=25x-9y$
$\therefore (5\sqrt{x}-3\sqrt{y})$ is rationalised by using its conjugate $(5\sqrt{x}+3\sqrt{y})$.