Aptitude Question ID: 107143

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

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


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