A) \[\sqrt{3}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[(2+\sqrt{3})\]
D) \[(2-\sqrt{3})\]
Correct Answer: A
Solution :
\[(\sqrt{1+a}+\sqrt{1-a})\] \[=\sqrt{{{\left( \sqrt{1+a}+\sqrt{1-a} \right)}^{2}}}\] \[=\sqrt{1+a+1-a+2\sqrt{(1+a)}(1-a)}\] \[=\sqrt{2+2\sqrt{1-{{a}^{2}}}}\] \[=\]\[\sqrt{2+2\sqrt{1-{{\left( \frac{\sqrt{5}}{2} \right)}^{2}}}}\] \[=\sqrt{2+2\sqrt{1-\frac{3}{4}}}\] \[=\sqrt{2+1=}\sqrt{3}\]
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