Aptitude Question ID: 107143

If (4+\sqrt{7}) is presented in the form of perfect square it will be equal to :
[A]\left ( 2+\sqrt{7} \right )^{2}
[B]\left ( \sqrt{3}+\sqrt{4} \right )^{2}
[C]\left [ \frac{\sqrt{7}}{2}+\frac{1}{2} \right ]^{2}
[D]\left \{ \frac{1}{\sqrt{2}}(\sqrt{7}+1) \right \}^{2}

\mathbf{\left \{ \frac{1}{\sqrt{2}}(\sqrt{7}+1) \right \}^{2}}
4+\sqrt{7} = \frac{8+2\sqrt{7}}{2}
= \frac{7+1+2\times \sqrt{7}\times 1}{2}
= \frac{(\sqrt{7})^{2}+(1)^{2}+2\times \sqrt{7}\times 1}{2}
= \frac{(\sqrt{7}+1)^{2}}{(\sqrt{2})^{2}}= \left \{ \frac{1}{\sqrt{2}}(\sqrt{7}+1) \right \}^{2}
Hence option [D] is correct answer.

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