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1 √ 9 − √ 8 − 1 √ 8 − √ 7 + 1 √ 7 − √ 6 − 1 √ 6 − √ 5 + 1 √ 5 − √ 4 = ? - Mathematics

MCQ

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

Options

  • 0

  • 1

  • `1/3`

  • 5

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Solution

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`

Concept: Simplification
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