# The ratio 216:x is equivalent to the ratio x^{2}:216. What is the value of x?

The ratio 216:x is equivalent to the ratio ${x}^{2}:216$. What is the value of x?
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Leonard Stokes

The ratio 216:x written as a fraction is 216/x.
The ratio x2:216 written as a fraction is $\frac{\left({x}^{2}\right)}{216}$
If the ratios are equivalent (which means they are equal), then:
$\frac{216}{x}=\frac{{x}^{2}}{216}$
$216×216=x×{x}^{2}$
$46,656={x}^{3}$
$3\sqrt{46,656}=3\sqrt{{x}^{6}}$
36=x