Question

Choose the correct answer from the alternative given.
$\sqrt{1+\sqrt{-3}}+\sqrt{1-\sqrt{-3}}$.

• A. $\sqrt{2}$
• B. $\sqrt{6}$
• C. $\sqrt{3}$
• D. Cannot be determined

Answer 1

The correct option is B $\sqrt{6}$

Squaring both sides.
1 + $\sqrt{-3}+1-\sqrt{-3}+2\sqrt{1+\sqrt{-3}}\sqrt{1-\sqrt{-3}}=x^2$
2 + 2$\sqrt{1^2(\sqrt{-3}}{)}^2$
2 + 2$\sqrt{1+3}$
2 + 2 $\times 2=x^2$
6 = $x^2$
x = $\sqrt{6}$