Question

$\text{What is the outcome after the denominator of}\frac{1}{\sqrt{5}+2}$ $\text{has been rationalized?}$

• A. $\sqrt{5}+2$
• B. $\sqrt{5}-2$
• C. $-\sqrt{5}-2$
• D. $-\sqrt{5}+2$

Answer 1

The correct option is B $\sqrt{5}-2$

$\frac{1}{\sqrt{5}+2}=\frac{1}{\sqrt{5}+2}\times \frac{\sqrt{5}-2}{\sqrt{5}-2}$

$=\frac{\sqrt{5}-2}{(\sqrt{5}{)}^2-2^2}$

$=\frac{\sqrt{5}-2}{5-4}$

$=\frac{\sqrt{5}-2}{1}$

$=\sqrt{5}-2$