For what positive number is the square root of the number the same as the number divided by $20$?

เฉลยละเอียด

[STEP]Setup the equation[/STEP]

Suppose the number is $n$. We have

$$\sqrt{n}=\frac{n}{20}$$

[STEP]Squaring both sides of the equation[/STEP]

\begin{eqnarray*}
\sqrt{n} & = & \frac{n}{20}\\
n & = & \frac{n^{2}}{400}\\
400n & = & n^{2}\\
n & = & 400.
\end{eqnarray*}

[ANS]Since $n\neq 0$ we have $n=400$.[/ANS]

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