Question

`1/(sqrt9-sqrt8) - 1/(sqrt8-sqrt7)+1/(sqrt7-sqrt6)-1/(sqrt6-sqrt5)+1/(sqrt5-sqrt4) = ?`

विकल्प

• 0

• 1

• `1/3`

• 5

Answer 1

5
Explanation:

`1/(sqrt9-sqrt8) - 1/(sqrt8-sqrt7)+1/(sqrt7-sqrt6)-1/(sqrt6-sqrt5)+1/(sqrt5-sqrt4)`

Multiplying by rationalisation factor in numerator and denominator of each term, we get

`(sqrt9+sqrt8)- (sqrt8+sqrt7)+(sqrt7+sqrt6)-(sqrt6+sqrt5)+(sqrt5+sqrt4)`

= `sqrt9+sqrt4= 3+2 = 5`