Question

By Rationalising the denominator ,find the value of $\frac{1}{2+\sqrt{3}}$ upto 2 significant figures.

• A. 0.23
• B. 0.27
• C. 0.37
• D. 0.72

Answer 1

The correct option is B

0.27

Given that $\frac{1}{2+\sqrt{3}}$

Rationalising factor of $2+\sqrt{3}$ is $2-\sqrt{3}$.

Multiplying both numerator and denominator by $2-\sqrt{3}$,
$=\frac{1}{2+\sqrt{3}}$ $\times$ $\frac{2-\sqrt{3}}{2-\sqrt{3}}$

= $\frac{2-\sqrt{3}}{(2{)}^2-\sqrt{(}3{)}^2}$

= $\frac{2-\sqrt{3}}{4-3}$

= $2-\sqrt{3}$

Taking the value of $\sqrt{3}$ = 1.732

= 2 - 1.732

= 0.268

Hence $\frac{1}{2+\sqrt{3}}$ = 0.27