Question

Rationalize the denominator of $\frac{1}{2-\sqrt{3}}$

• A. 2 + √3
• B. 4 + √3
• C. 3 + 2√3
• D. 2 + 2√3

Answer 1

The correct option is A

2 + √3

If the denominator is of the form a + b, where a or b or both are irrational, then to make it rational, multiply and divide by a - b.

$\frac{1}{2-\sqrt{3}}$=$\frac{2+\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}$=$\frac{2+\sqrt{3}}{4-3}$=$2+\sqrt{3}$