A) \[\sqrt{2}\]
B) \[\sqrt{7}\]
C) \[\sqrt{5}\]
D) \[2\sqrt{5}\]
Correct Answer: C
Solution :
Expression\[=\sqrt{2}+\sqrt{7-2\sqrt{10}}\] \[=\sqrt{2}+\sqrt{7-2\sqrt{5}\times \sqrt{2}}\] \[=\sqrt{2}+\sqrt{{{(\sqrt{5})}^{2}}+{{(\sqrt{2})}^{2}}-2\times \sqrt{5}\times \sqrt{2}}\] \[=\sqrt{2}+\sqrt{{{(\sqrt{5}-\sqrt{2})}^{2}}}\] \[=\sqrt{2}+\sqrt{5}-\sqrt{2}=\sqrt{5}\]
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