Simplify the expression
\[\frac{1}{\sqrt{2}} +\frac{3}{\sqrt{8}} + \frac{6}{\sqrt{32}}.\]

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).

step-by-step explanation:

divide, then simplify your answer.

1. make -15.66 ÷   5.8 a fraction. then divide.

2. simplify.  

3. final answer.