Find the value of $\sqrt{2+\sqrt{3}} +\sqrt{2-\sqrt{3}}$.
Answer & explanation
Correct answer: option 1
Find the value of $\sqrt{2+\sqrt{3}} +\sqrt{2-\sqrt{3}}$
Multiply and divide the equation by 2
= $\sqrt{2+\sqrt{3}} +\sqrt{2-\sqrt{3}}$
= $\frac{\sqrt{4+2\sqrt{3}}{2}$ + $\frac{\sqrt{4-2\sqrt{3}}{2}$
= $\frac{\sqrt{(2+\sqrt{3})^2}{(\sqrt{2})^2}$ + $\frac{\sqrt{(2-\sqrt{2})^2}{(\sqrt{3})^2}$
= $\frac{2 + \sqrt {3}}{\sqrt {2}}$ + $\frac{2 - \sqrt {3}}{\sqrt {2}}$
= $\frac{2\sqrt {3}}{\sqrt {2}}$ = $\sqrt{6}$