8 = 2³ and 32 = 2⁵, so
√(8) = √(2²•2) = 2√(2)
√(32) = √(2⁴•2) = 2²√(2) = 4√(2)
Then
1/√(2) + 3/√(8) + 6/√(32)
= 1/√(2) + 3/(2√(2)) + 6/(4√(2))
= 4/(4√(2)) + 6/(4√(2)) + 6/(4√(2))
= 16/(4√(2))
= 4/√(2)
Optional step: Rationalize the denominator by multiply this by √(2)/√(2) to get
4/√(2) • √(2)/√(2) = (4√(2))/2 = 2√(2)
which you can also write as √(8).
