Rationalise the denominator in $\dfrac{2}{1-\sqrt{2}}$
$2+2\sqrt{2}$
$2-2\sqrt{2}$
$-2+2\sqrt{2}$
$-2-2\sqrt{2}$
Explanation:
$\dfrac{2}{1-\sqrt{2}} = \dfrac{2}{1-\sqrt{2}} \times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}$ [multiply the numerator and denominator by $1+\sqrt{2}$]
=$\dfrac{2+2\sqrt{2}}{1-2}$
=$\dfrac{2+2\sqrt{2}}{-1}$
=$-2-2\sqrt{2}$
$\dfrac{2}{1-\sqrt{2}} = \dfrac{2}{1-\sqrt{2}} \times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}$ [multiply the numerator and denominator by $1+\sqrt{2}$]
=$\dfrac{2+2\sqrt{2}}{1-2}$
=$\dfrac{2+2\sqrt{2}}{-1}$
=$-2-2\sqrt{2}$