## 1.9 Rationalising Factors [15m]

RATIONALIZING the DENOMINATOR

The process of converting an expression whose denominator is an irrational number to an equivalent expression whose denominator is a rational number is called rationalising the denominator. To do this, we multiply and divide the expression by the rationalising factor of the denominator.

EXERCISE: Rationalise the denominators of the following:

(i) $\frac{1}{\sqrt{7}}$   (ii) $\frac{1}{\sqrt{7}-\sqrt{6}}$   (iii) $\frac{1}{\sqrt{5}+\sqrt{2}}$   (iv) $\frac{1}{\sqrt{7}-2}$

SELF PRACTICE: Rationalise the denominators of the following:

(i) $\frac{1}{\sqrt{13}}$
(ii) $\frac{1}{\sqrt{5}-\sqrt{3}}$
(iii) $\frac{1}{\sqrt{6}+\sqrt{3}}$
(iv) $\frac{1}{\sqrt{11}-3}$

Discussion