1.

The value of \(\frac{1}{{\sqrt 7- \sqrt 6 }} - \frac{1}{{\sqrt 6- \sqrt 5 }} + \frac{1}{{\sqrt 5- 2}} - \frac{1}{{\sqrt 8- \sqrt 7 }} + \frac{1}{{3 - \surd 8}}\) is1). 52). 13). 74). 0

Answer»

Using the CONCEPT a – b = (√a - √b) (√a + √b)

MULTIPLY and dividing each fraction by its conjugate we get,

$(\frac{1}{{\sqrt 7- \sqrt 6 }} \TIMES \frac{{\sqrt 7+ {\rm{\;}}\sqrt 6 }}{{\sqrt 7+ {\rm{\;}}\sqrt 6 }} - \frac{1}{{\sqrt 6- \sqrt 5 }} \times \frac{{\sqrt 6+ {\rm{\;}}\sqrt 5 }}{{\sqrt 6+ {\rm{\;}}\sqrt 5 }} + \frac{1}{{\sqrt 5- 2}} \times \frac{{\sqrt 5+ {\rm{\;}}2}}{{\sqrt 5+ {\rm{\;}}2}} - \frac{1}{{\sqrt 8- \sqrt 7 }} \times \frac{{\sqrt 8 {\rm{\;}} + {\rm{\;}}\sqrt 7 }}{{\sqrt 8+ \sqrt 7 }} + \frac{1}{{3 - \sqrt 8 }} \times \frac{{3{\rm{\;}} + {\rm{\;}}\sqrt 8 }}{{3{\rm{\;}} + \sqrt 8 }})$

= √7 + √6 - √6 - √5 + √5 + 2 - √8 -√7 + 3 + √8

= 5


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