$$\left( {4 + \sqrt 7 } \right),$$ 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
Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
Join The Discussion