Question

Find all the real fourth roots of 256/2401. I know the right answer is +/-4/7, I just need to know how to get there. The answer I picked had +/-4/7 and +/-16/49

Answer 1

Let x be the real root
\[x^4=\frac{ 256 }{ 2401 },\left( x^2 \right)^2=\left( \frac{ 16 }{ 49 } \right)^2\]
taking square root
\[x^2=\pm \frac{ 16 }{ 49 }\]
as x is real so x^2 is positive.
\[x^2=\frac{ 16 }{ 49 }=\left( \frac{ 4 }{ 7 } \right)^2\]
again taking the squreroot
\[x=\pm \frac{ 4 }{ 7 }\]

Answer 2

Wow, thank you! I see my mistake now; I just thought I was supposed to give them both fractions. Like a "simplified and actual solution" type thing