SOLUTION: if a and b are positive integers and (a^(1/2) * b^(1/3)) = 432, what is the value of ab?

Algebra ->  Expressions-with-variables -> SOLUTION: if a and b are positive integers and (a^(1/2) * b^(1/3)) = 432, what is the value of ab?      Log On


   

Question 375846: if a and b are positive integers and (a^(1/2) * b^(1/3)) = 432, what is the value of ab?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E%281%2F2%29%2A+b%5E%281%2F3%29+=+432
Square both sides.
a%5E%283%2F2%29%2Ab=432%5E3
Cube both sides.
a%5E3b%5E2=432%5E6
Look at factors of 432,
a%5E3b%5E2=%282%5E4%2A3%5E3%29%5E6
a%5E3b%5E2=2%5E24%2A3%5E18
Two solutions:
a%5E3=2%5E24, highlight%28+a=2%5E8%29
b%5E2=3%5E18, highlight%28b=3%5E9%29
or
a%5E3=3%5E18, highlight_green%28a=3%5E6%29
b%5E2=2%5E24, highlight_green%28b=2%5E12%29