Question

State True or False, if the expression $\frac{4}{\sqrt{5}-1}$$=\sqrt{5}+1$ after rationalising the denominator.

• A. True
• B. False

Answer 1

The correct option is A True

As given $\frac{4}{\sqrt{5}-1}$

Multiply and divided by $\sqrt{5}+1$

$=\frac{4}{\sqrt{5}-1}\times \frac{\sqrt{5}+1}{\sqrt{5}+1}$

$=\frac{4(\sqrt{5}+1)}{{\left(\sqrt{5}\right)}^2-1}$

$=\frac{4(\sqrt{5}+1)}{5-1}$

$=\frac{4(\sqrt{5}+1)}{4}$

$=\sqrt{5}+1$

Hence the answer is True.