MHB Cube Roots: Solve A+B=C Problem Easily

[JamieLam]

This is a simple question. The problem I'm facing is A cube plus B cube = 22 C cube
A cube plus B cube over 22 = C cube
At this junction I like to ask if I want to cuberoots both sides, will the 22 be cube root as well? I'm sorry to bother since I forgot my basics. I don't want solutions to the problem. I only want to know about the cube rooting. Thanks!

 

[Fantini]

Yes, you will have to cube the 22 as well. What you have is

$$\frac{A^3 + B^3}{22} = C^3.$$

If you cube both sides you realize that 22 can't be neglected. :)

 

[HallsofIvy]

Fantini said "cube" but I am sure he meant "cube root".

If C^3= \frac{A^3+ B^3}{22}
then C= \sqrt[3]{\frac{A^3+ B^3}{22}}= \frac{\sqrt[3]{A^3+ B^3}}{\sqrt[3]{22}}.

I hope you understand that \sqrt[3]{A^3+ B^3} is NOT the same a A+ B!