# How do you solve sqrt(x^3) = 8?

Feb 4, 2016

Square both sides: ${x}^{3} = 64$. Then take the cube root of both sides: $x = 4$.

#### Explanation:

I'm not sure a lot more explanation is needed: we do what we always do in algebra. That is, seek to make one pronumeral, in this case $x$, the subject of the equation by doing the same things to both sides of the equation.

(This is because, if the equals sign is to remain true, we must do the same thing to both sides at each step.)

Feb 4, 2016

You can also use the rule ${\sqrt[m]{a}}^{n}$ = ${a}^{\frac{n}{m}}$

#### Explanation:

$\sqrt{{x}^{3}}$ = 8

${\left({x}^{3}\right)}^{\frac{1}{2}}$ = 8

${x}^{\frac{3}{2}}$ = 8

${x}^{3}$ = ${8}^{2}$

${x}^{3}$ = 64

x = 4

Pretty much, just a more in-depth proof of the earlier solution. Hopefully this helps!