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Simplify: 1/sqrt[11-2sqrt30]-3/sqrt[7-2...

Simplify: `1/sqrt[11-2sqrt30]`-`3/sqrt[7-2sqrt10]`-`4/sqrt[8+4sqrt3]`

Text Solution

Verified by Experts

`1/sqrt(11-2sqrt30) = 1/sqrt(11-2sqrt30)xxsqrt(11+2sqrt30)/sqrt(11+2sqrt30)`
`=sqrt(11+2sqrt30)/(121-120) = sqrt(11+2sqrt30)`

`3/(sqrt(7-2sqrt10)) = 3/sqrt(7-2sqrt10)xxsqrt(7+2sqrt10)/(sqrt(7+2sqrt10)`
`=(3sqrt(7+2sqrt10))/(49-40) = sqrt(7+2sqrt10)`

`4/sqrt(8+4sqrt3) = 4/sqrt(8+4sqrt3)xxsqrt(8-4sqrt3)/sqrt(8-4sqrt3)`
`=(4sqrt(8-4sqrt3))/(64-48) = sqrt(8-4sqrt3)= sqrt(8-2sqrt12)`

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