The value of $$\frac{1}{{\sqrt 7 - \sqrt 6 }} - $$ $$\frac{1}{{\sqrt 6 - \sqrt 5 }} + $$ $$\frac{1}{{\sqrt 5 - 2 }} - $$ $$\frac{1}{{\sqrt 8 - \sqrt 7 }} + $$ $$\frac{1}{{3 - \sqrt 8 }} = ?$$
A. 0
B. 1
C. 5
D. 7
Answer: Option C
Solution(By Examveda Team)
$$\frac{1}{{\sqrt 7 - \sqrt 6 }} - $$ $$\frac{1}{{\sqrt 6 - \sqrt 5 }} + $$ $$\frac{1}{{\sqrt 5 - 2 }} - $$ $$\frac{1}{{\sqrt 8 - \sqrt 7 }} + $$ $$\frac{1}{{3 - \sqrt 8 }} = ?$$⇒ Rationalising,
$$ \Rightarrow \frac{{\sqrt 7 + \sqrt 6 }}{{\left( {\sqrt 7 + \sqrt 6 } \right)\left( {\sqrt 7 - \sqrt 6 } \right)}} - $$ $$\frac{1}{{\left( {\sqrt 6 - \sqrt 5 } \right)}} \times $$ $$\frac{{\left( {\sqrt 6 + \sqrt 5 } \right)}}{{\left( {\sqrt 6 + \sqrt 5 } \right)}} + $$ $$\frac{{\sqrt 5 + \sqrt 4 }}{{\left( {\sqrt 5 - \sqrt 4 } \right)\left( {\sqrt 5 + \sqrt 4 } \right)}} - $$ $$\frac{{\left( {\sqrt 8 + \sqrt 7 } \right)}}{{\left( {\sqrt 8 - \sqrt 7 } \right)\left( {\sqrt 8 + \sqrt 7 } \right)}} + $$ $$\frac{{\left( {\sqrt 9 + \sqrt 8 } \right)}}{{\left( {\sqrt 9 + \sqrt 8 } \right)\left( {\sqrt 9 - \sqrt 8 } \right)}}$$
$$ \Rightarrow \frac{{\sqrt 7 + \sqrt 6 }}{1} - $$ $$\frac{{\left( {\sqrt 6 + \sqrt 5 } \right)}}{1} + $$ $$\frac{{\left( {\sqrt 5 + \sqrt 4 } \right)}}{1} - $$ $$\frac{{\left( {\sqrt 8 + \sqrt 7 } \right)}}{1} + $$ $$\frac{{\left( {\sqrt 9 + \sqrt 8 } \right)}}{1}$$
$$ \Rightarrow \sqrt 7 \,+ $$ $$\sqrt 6 \,- $$ $$\sqrt 6 \,- $$ $$\sqrt 5 \,+ $$ $$\sqrt 5 \,+ $$ $$\sqrt 4 \,- $$ $$\sqrt 8 \,- $$ $$\sqrt 7 \,+ $$ $$\sqrt 9 \,+ $$ $$\sqrt 8 $$
$$\eqalign{ & \Rightarrow \sqrt 4 + \sqrt 9 \cr & \Rightarrow 2 + 3 \cr & \Rightarrow 5 \cr} $$
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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