Answer
$y=125$
Work Step by Step
The given equation is
$\Rightarrow \sqrt[3]{y}-4=1$
Add $4$ to each side.
$\Rightarrow \sqrt[3]{y}-4+4=1+4$
Simplify.
$\Rightarrow \sqrt[3]{y}=5$
Cube each side of the equation.
$\Rightarrow (\sqrt[3]{y})^3=5^3$
Simplify.
$\Rightarrow y=125$
Check $y=125$.
$\Rightarrow \sqrt[3]{y}-4=1$
$\Rightarrow \sqrt[3]{125}-4=1$
$\Rightarrow \sqrt[3]{5^3}-4=1$
$\Rightarrow 5-4=1$
$\Rightarrow 1=1$
True.
Hence, the solution is $y=125$.
