Answer
The solution is $x=256$
Work Step by Step
$\sqrt{x}-3\sqrt[4]{x}-4=0\hspace{0.7cm} \color{blue}{\text{Given equation}}$
$x^{1/2}-3x^{1/4}-4=0$
$(x^{1/4})^2-3x^{1/4}-4=0$
$W^2-3W-4=0\hspace{3.3cm} \color{blue}{\text{Let } W=x^{1/4}}$
$(W+1)+(W-4)=0\hspace{2.3cm} \color{blue}{\text{Factor}}$
$W+1=0\hspace{0.5cm}or\hspace{0.5cm}W-4=0\hspace{1.3cm} \color{blue}{\text{Zero-Product Property}}$
$W=-1\hspace{1.5cm}W=4\hspace{1.99cm} \color{blue}{\text{Solve}}$
Now change $W$ back into the correspondimg values of $x$
$x^{1/4}=-1\hspace{1.5cm}x^{1/4}=4$
$x=\text{due to -ve sign the solution rejects}\hspace{1.5cm}x=256$
The solution is $x=256$
