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1/(3-sqrt8)-1/(sqrt8-sqrt7)+1/(sqrt7-sqr...

`1/(3-sqrt8)-1/(sqrt8-sqrt7)+1/(sqrt7-sqrt6)-1/(sqrt6-sqrt5)+1/(sqrt5-2)=5`

Text Solution

Verified by Experts

We are given to prove :`1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2=5`
Now,
`1/3-√8 = 3+√8`,
`1/√8-√7 = √8+√7`,
`1/√7-√6 = √7+√6`,
`1/√6-√5 = √6+√5`,
`1/√5-2 = √5+2`
∴ `1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2`
= `3+√8-√8√7+√7+√6√6√5+√5+2`
=`3+2 = 5`
Hence proved.
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