The simplified value of $$\left( {\sqrt 6 + \sqrt {10} - \sqrt {21} - \sqrt {35} } \right)\left( {\sqrt 6 - \sqrt {10} + \sqrt {21} - \sqrt {35} } \right){\text{is}}$$
A. 13
B. 12
C. 11
D. 10
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & \left( {\sqrt 6 + \sqrt {10} - \sqrt {21} - \sqrt {35} } \right)\left( {\sqrt 6 - \sqrt {10} + \sqrt {21} - \sqrt {35} } \right) \cr & = \left\{ {\left( {\sqrt 6 - \sqrt {35} } \right) + \left( {\sqrt {10} - \sqrt {21} } \right)} \right\}\left\{ {\left( {\sqrt 6 - \sqrt {35} } \right) - \left( {\sqrt {10} - \sqrt {21} } \right)} \right\} \cr & = {\left( {\sqrt 6 - \sqrt {35} } \right)^2} - {\left( {\sqrt {10} - \sqrt {21} } \right)^2} \cr & = \left( {6 - 35 - 2\sqrt {210} } \right) - \left( {10 + 21 - 2\sqrt {210} } \right) \cr & = 41 - 2\sqrt {210} - 31 + 2\sqrt {210} \cr & = 41 - 31 \cr & = 10 \cr} $$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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