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Question
Simplify.
`sqrt 216 - 5 sqrt 6 +sqrt 294 -3/sqrt6`
Solution
`sqrt 216 - 5 sqrt 6 +sqrt 294 -3/sqrt6`
`= sqrt(36 xx 6) -5 sqrt 6 + sqrt(49 xx 6) -3/sqrt6 xx sqrt 6/sqrt 6`
`= 6sqrt 6 - 5sqrt 6 + 7sqrt6 -(3sqrt6)/6`
`= 6sqrt 6 - 5sqrt 6 + 7sqrt6 -(sqrt6)/2`
`= (6 - 5 + 7 - 1/2) sqrt6`
= `(8/1 - 1/2) sqrt6`
= `((16-1)/2) sqrt6`
`= 15/2sqrt6`
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