Question

4√22/4√2*4√12/3√18

This reads: 4 square root 22 over 4 square root 2 multiply by 4 square root 12 over 3 square root 18

Answer 1

ahhh, so 4√22/4√2*4√12/3√18

is really
(4√22)/(4√2)*(4√12)/(3√18)

this same question was posted twice yesterday, and even after requests for clarification, confusion remained because of a lack of brackets.

so now we have
(4√22)/(4√2)*(4√12)/(3√18)
= (√11) * (8√3)/(9√2)
= 8√33/(9√2)
rationalizing by multiplying top and bottom by √2
= 8√66/18
= 4√66/9

(evaluating the original on a calculator and evaluating the final result yields the same decimal answer.)

or without having to rationalize I could have done this:

= √22/√2 * 8√3/(9√2)
= 8√66/18
= 4√66/9