How do you solve the following? 6√1/6 - √2/3 the answer at the back of the book says 6√2, but I'm not sure how to get there.

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Answer 1 · 2014-11-01T12:33:27

Since

#6sqrt{1/6}=6/sqrt{6}={(sqrt{6})^2}/sqrt{6}=sqrt{6}#

and

#sqrt{2/3}=sqrt{2}/sqrt{3}cdot{sqrt{3}}/{sqrt{3}}=sqrt{6}/3#,

we have

#6sqrt{1/6}-sqrt{2/3}=sqrt{6}-{sqrt{6}}/3=(1-1/3)sqrt{6}=2/3sqrt{6}#.

I hope that this was helpful.