How can I solve the following question?

Question

How can I solve the following problem?

$4\cdot 2\sqrt{x}=x^2$

Answer 1

Have you tried squaring both sides?

Answer 2

HINT: $4\cdot2=8=2^3$, and $\dfrac{x^2}{\sqrt{x}}=\dfrac{x^2}{x^{1/2}}=x^{2-\frac12}=\ldots$

Answer 3

$4*2\sqrt{x}=x^2$; for $\sqrt{x}$ to be meaningful $x \ge 0$.

$8x^{\frac 12} =(x^{\frac 12})^4$; if $x^{\frac 12}=0$ then $8*0=0^4$ and $x =0$

$8 = (x^{\frac 12})^3$; if $x^{\frac 12} \ne 0$.

$\sqrt[3]{8} = x^{\frac 12}$

$2 = x^{\frac 12}$

$2^2 = x$

$x=4$

So $x = 4$ or $x=0$.