The simplification value of $$\left( {\sqrt 3 + 1} \right)$$ $$\left( {10 + \sqrt {12} } \right)$$ $$\left( {\sqrt {12} - 2} \right)$$ $$\left( {5 - \sqrt 3 } \right)$$ is = ?
A. 16
B. 88
C. 176
D. 132
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \left( {\sqrt 3 + 1} \right)\left( {10 + \sqrt {12} } \right)\left( {\sqrt {12} - 2} \right)\left( {5 - \sqrt 3 } \right) \cr & \Rightarrow \left( {\sqrt 3 + 1} \right)\left( {10 + 2\sqrt 3 } \right)\left( {2\sqrt 3 - 2} \right)\left( {5 - \sqrt 3 } \right) \cr} $$$$ \Rightarrow \left( {\sqrt 3 + 1} \right) \times $$ $$2\left( {5 + \sqrt 3 } \right) \times $$ $$2\left( {\sqrt 3 - 1} \right)$$ $$\left( {5 - \sqrt 3 } \right)$$
$$\eqalign{ & \Rightarrow 4\left( {\sqrt 3 + 1} \right)\left( {\sqrt 3 - 1} \right)\left( {5 + \sqrt 3 } \right)\left( {5 - \sqrt 3 } \right) \cr & \Rightarrow 4\left[ {{{\left( {\sqrt 3 } \right)}^2} - {1^2}} \right]\left[ {{{\left( 5 \right)}^2} - {{\left( {\sqrt 3 } \right)}^2}} \right] \cr & \Rightarrow 4 \times 2 \times 22 \cr & \Rightarrow 176 \cr} $$
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
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