Question

find the value of 1\√3+√4+1\√4+√5+1\√5+√6+1\√6+√7+1\√7+√8+1\√8+√9

Answer 1

Answer:

Step-by-step explanation:

Prove that (1 / √4 + √5) + (1 / √5 + √6) + (1 / √6 + √7) + (1 / √7 + √8) + (1 / √8 + √9) = 1

Class-IX Math

Sol:

1 / (√4 + √5)

= [1 / (√4 + √5)] x [(√4 - √5)/(√4 - √5)]

= (√4 - √5) / (√4)2 - (√5)2

= (√4 - √5) / 4 - 5

= (√4 - √5) / (-1)

= (√5 - √4)

(1 / √5 + √6)

= [1 / (√5 + √6)] x [(√5 - √6)/(√5 - √6)]

= (√5 - √6) / (√5)2 - (√6)2

= (√5 - √6) / 5 - 6

= (√5 - √6) / (-1)

= (√6 - √5)

Similarly,

(1 / √6 + √7) = (√7 - √6)

(1 / √7 + √8) = (√8 - √7)

(1 / √8 + √9) = (√9 - √8)

(1 / √4 + √5) + (1 / √5 + √6) + (1 / √6 + √7) + (1 / √7 + √8) + (1 / √8 + √9)

= (√5 - √4) + (√6 - √5) + (√7 - √6) + (√8 - √7) + (√9 - √8)

= 3 - 2

= 1

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Answer 2

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