$\sqrt{y^4} = y^2$
$\begin{equation*} \begin{cases} y^4 ≥ 0 &\\ y^2 ≥ 0 & \end{cases} \end{equation*}$
y ∈ R

$\sqrt{x^{12}} = x^6$
$\begin{equation*} \begin{cases} x^{12} ≥ 0 &\\ x^6 ≥ 0 & \end{cases} \end{equation*}$
x ∈ R

$\sqrt{x^6} = x^3$
$\begin{equation*} \begin{cases} x^{6} ≥ 0 &\\ x^3 ≥ 0 & \end{cases} \end{equation*}$
x ≥ 0

$\sqrt{c^{10}} = -c^5$
$\begin{equation*} \begin{cases} c^{10} ≥ 0 &\\ -c^5 ≥ 0 & \end{cases} \end{equation*}$
c ≤ 0

$\sqrt{a^{14}} = -a^7$
$\begin{equation*} \begin{cases} a^{14} ≥ 0 &\\ -a^7 ≥ 0 & \end{cases} \end{equation*}$
a ≤ 0

$\sqrt{b^8} = b^4$
$\begin{equation*} \begin{cases} b^{8} ≥ 0 &\\ b^4 ≥ 0 & \end{cases} \end{equation*}$
b ∈ R