Practice | Hashtable

Home > Practice > Arithmetic Aptitude > Surds and Indices > Miscellaneous

1. $\sqrt{8 - 2 \sqrt{15}}$ is equal to = ?

A. $3 - \sqrt{5}$

B. $\sqrt{5} - \sqrt{3}$

C. $5 - \sqrt{3}$

D. $\sqrt{5} + \sqrt{3}$

Solution:

\begin{aligned} \sqrt{8 - 2 \sqrt{15}} \\ = \sqrt{5 + 3 - 2 \times \sqrt{5} \times \sqrt{3}} \\ = \sqrt{{(\sqrt{5})}^{2} + {(\sqrt{3})}^{2} - 2 \times \sqrt{5} \times \sqrt{3}} \\ = \sqrt{{(\sqrt{5} - \sqrt{3})}^{2}} \\ = (\sqrt{5} - \sqrt{3}) \end{aligned}

You must login to add comments. Login now.