simplify: square root of 5 + square root of 20 - square root of 27 + square root of 147.

simplify: 6/4square root of 2

sqrt 5 + sqrt 20 - sqrt 27 + sqrt 147
= sqrt 5 + sqrt (4*5) - sqrt (3*9) + sqrt (49*3)
= 3 sqrt 5 - 3 sqrt 3 + 7 sqrt 3
= 3 sqrt 5 + 4 sqrt 3

Your second problem is ambiguous. Do you mean (6/4)*sqrt 2 or 6/(4 sqrt 2) ?
In either case, you can change the 6/4 to 3/2

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