The simplified form of $$\frac{2}{{\sqrt 7 + \sqrt 5 }} + $$ $$\frac{7}{{\sqrt {12} - \sqrt 5 }} - $$ $$\frac{5}{{\sqrt {12} - \sqrt 7 }}$$ is = ?
A. 5
B. 2
C. 1
D. 0
Answer: Option D
Solution(By Examveda Team)
$$\frac{2}{{\sqrt 7 + \sqrt 5 }} + \frac{7}{{\sqrt {12} - \sqrt 5 }} - \frac{5}{{\sqrt {12} - \sqrt 7 }}$$$$ = \frac{2}{{\sqrt 7 + \sqrt 5 }} \times $$ $$\frac{{\sqrt 7 - \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} + $$ $$\frac{7}{{\sqrt {12} - \sqrt 5 }} \times $$ $$\frac{{\sqrt {12} + \sqrt 5 }}{{\sqrt {12} + \sqrt 5 }} - $$ $$\left( {\frac{5}{{\sqrt {12} - \sqrt 7 }} \times \frac{{\sqrt {12} + \sqrt 7 }}{{\sqrt {12} + \sqrt 7 }}} \right)$$
$$ = \frac{{2\left( {\sqrt 7 - \sqrt 5 } \right)}}{2} + $$ $$\frac{{7\left( {\sqrt {12} + \sqrt 5 } \right)}}{7} - $$ $$\frac{{5\left( {\sqrt {12} + \sqrt 7 } \right)}}{5}$$
$$\eqalign{ &= \sqrt 7 - \sqrt 5 + \sqrt {12} + \sqrt 5 - \sqrt {12} - \sqrt 7 \cr &= 0 \cr} $$
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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