Write the least (smallest) rationalising factor of :

(i) $\sqrt{12}$

(ii) $2\sqrt{12}$

(iii) $\sqrt{18}$

(iv) $\dfrac{1}{\sqrt{5}}$

(v) $\sqrt\dfrac{2}{3}$

(i) $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt3$

And, $2\sqrt3 \times \sqrt{3}$ = 6, which is a rational number.

Hence, the least (smallest) rationalising factor of $\sqrt{12} = \sqrt3$.

(ii) $2\sqrt{12} = 2\sqrt{4 \times 3} = 2 \times 2\sqrt3 = 4\sqrt3$

And, $4\sqrt3 \times \sqrt{3} = 12$, which is a rational number.

Hence, the least (smallest) rationalising factor of $2\sqrt{12} = \sqrt3$.

(iii) $\sqrt{18} = \sqrt{3 \times 3 \times 2} = 3\sqrt2$

And, $3\sqrt2 \times \sqrt{2} = 6$, which is a rational number.

Hence, the least (smallest) rationalising factor of $\sqrt{18} = \sqrt{2}$.

(iv) $\dfrac{1}{\sqrt{5}} \times \sqrt{5}$ = 1, which is a rational number.

Hence, the least (smallest) rationalising factor of $\dfrac{1}{\sqrt{5}} = \sqrt{5}$.

(v) $\sqrt\dfrac{2}{3} \times \sqrt\dfrac{2}{3} = \dfrac{2}{3}$, which is a rational number.

Hence, the least (smallest) rationalising factor of $\sqrt\dfrac{2}{3} = \sqrt\dfrac{2}{3}$.