A) \[\sqrt{7}-\sqrt{3}\]
B) \[\sqrt{6}-\sqrt{3}\]
C) \[\sqrt{7}-\sqrt{5}\]
D) \[\sqrt{7}-\sqrt{2}\]
Correct Answer: D
Solution :
\[\sqrt{9-4\sqrt{14}}\,\,=\,\,\sqrt{7+2-2\sqrt{7\times 2}}\] \[=\sqrt{{{(\sqrt{7})}^{2}}+{{(\sqrt{2})}^{2}}-2\sqrt{7}\times \sqrt{2}}\] \[=\,\,\sqrt{{{(\sqrt{7}-\sqrt{2})}^{2}}}\,\,\,\,\,(\because \,\,\,{{a}^{2}}+{{b}^{2}}-2ab={{(a-b)}^{2}})\] \[=\,\,\,\sqrt{\mathbf{7}}\,-\,\sqrt{\mathbf{2}}\]
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