Rationalising Denominators

Rationalising Denominators simplifies the fractions by multiplying the conjugates of the denominators.

Worked Example of Rationalising Denominators

Simplify \( \displaystyle\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \cdots + \frac{1}{\sqrt{99} + \sqrt{100}} \).