The Rationalising factor of \(\frac{1}{5-\sqrt3}\) is A) 5 + √3B)

1.	The Rationalising factor of \(\frac{1}{5-\sqrt3}\) is A) 5 + √3B)√3 - 5C) \(\frac{1}{5+\sqrt3}\)D) \(\frac{1}{\sqrt3 - 5}\)
Answer» Correct option is (C) \(\frac{1}{5+\sqrt{3}}\) \(\because\) \(\frac{1}{5-\sqrt{3}}\times\frac{1}{5+\sqrt{3}}\) \(=\frac{1}{(5-\sqrt{3})(5+\sqrt{3})}\) \(=\frac{1}{5^2-(\sqrt3)^2}\) \(=\frac1{25-3}\) \(=\frac1{22}\) which is a rational number. \(\therefore\) Rationalising factor of \(\frac{1}{5-\sqrt{3}}\) is \(\frac{1}{5+\sqrt{3}}.\) Correct option is C) \(\frac{1}{5+\sqrt3}\)

The Rationalising factor of \(\frac{1}{5-\sqrt3}\) is A) 5 + √3B)√3 - 5C) \(\frac{1}{5+\sqrt3}\)D) \(\frac{1}{\sqrt3 - 5}\)

Answer»

Correct option is (C) \(\frac{1}{5+\sqrt{3}}\)

\(\because\) \(\frac{1}{5-\sqrt{3}}\times\frac{1}{5+\sqrt{3}}\) \(=\frac{1}{(5-\sqrt{3})(5+\sqrt{3})}\)

\(=\frac{1}{5^2-(\sqrt3)^2}\) \(=\frac1{25-3}\)

\(=\frac1{22}\) which is a rational number.

\(\therefore\) Rationalising factor of \(\frac{1}{5-\sqrt{3}}\) is \(\frac{1}{5+\sqrt{3}}.\)

Correct option is C) \(\frac{1}{5+\sqrt3}\)