$$\left( {4 + \sqrt 7 } \right),$$ expressed as a perfect square, is equal to = ?
A. $${\left( {2 + \sqrt 7 } \right)^2}$$
B. $${\left( {\frac{{\sqrt 7 }}{2} + \frac{1}{2}} \right)^2}$$
C. $$\left\{ {\frac{1}{2}{{\left( {\sqrt 7 + 1} \right)}^2}} \right\}$$
D. $$\left( {\sqrt 3 + \sqrt 4 } \right)$$
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & \left( {4 + \sqrt 7 } \right) \cr & = \frac{7}{2} + \frac{1}{2} + 2 \times \frac{{\sqrt 7 }}{{\sqrt 2 }} \times \frac{1}{{\sqrt 2 }} \cr & = {\left( {\frac{{\sqrt 7 }}{{\sqrt 2 }}} \right)^2} + {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} + 2 \times \frac{{\sqrt 7 }}{{\sqrt 2 }} \times \frac{1}{{\sqrt 2 }} \cr & = {\left( {\frac{{\sqrt 7 }}{{\sqrt 2 }} + \frac{1}{{\sqrt 2 }}} \right)^2} \cr & = \frac{1}{2}{\left( {\sqrt 7 + 1} \right)^2} \cr} $$This Question Belongs to Arithmetic Ability >> Surds And Indices
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