Question

By rationalising the denominator of \(\frac{1}{\sqrt{3}}\), we get __________

(a) \(\frac{\sqrt{3}}{3}\)

(b) \(\sqrt{3}\)

(c) \(\frac{3}{\sqrt{3}}\)

(d) \(3\sqrt{3}\)

This question was posed to me at a job interview.

The question is from Representing Real Numbers on the Number Line & Real Numbers Operations in division Number Systems of Mathematics – Class 9

Answer 1

The correct option is (a) \(\frac{\sqrt{3}}{3}\)

Explanation: When the denominator of an expression contains a term with a square root, the process of converting it to an equivalent expression whose denominator is a rational number is called rationalising the denominator.

By multiplying \(\frac{1}{\sqrt{3}}\) by \(\frac{\sqrt{3}}{\sqrt{3}}\), we will get same expression since \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1.

Therefore, \(\frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}} * (\frac{\sqrt{3}}{\sqrt{3}}) = \frac{\sqrt{3}}{3}\).