Rationalize the denominator of:\(1/(√2+√8+√32)\). The answer can be written as \((√A)/B\), where A and B are integers. Find the minimum possible value of A+B.

Keihaku Dec 7, 2022

#1**+1 **

1/(sqrt(2) + sqrt(8) + sqrt(32))

= 1/(sqrt(2) + 4*sqrt(2) + 16*sqrt(2))

= 1/(21*sqrt(2))

= sqrt(2)/(21*sqrt(2)*sqrt(2))

= sqrt(2)/42

A + B = 44

Guest Dec 7, 2022

#3**+1 **

I am not going to just give you the answer, but i can help you if you are interested.

8 = 4 (wich is a squared number) * 2

so

\(\sqrt8=\sqrt4*\sqrt2=2*\sqrt2 = 2\sqrt2\)

Now you simplify sqrt 32 in the same way. (Show me if you are not sure of your answer)

THEN simplify the denominator (bootom)

THEN show what you get for the bottom.

Melody Dec 7, 2022