Simplify Square Root Expression $\sqrt{125} - \sqrt{5}$ $\sqrt{125}-\sqrt5$ simplify it.
I thought it would be $\sqrt {5\cdot5\cdot5}-\sqrt 5$ which would be the square root of 25 which is 5 but it is not.
Can you show how to simplify this?

Starting from where you left off:
$$
\begin{eqnarray}
\sqrt{125}-\sqrt5
&=& \sqrt {5\cdot5\cdot5} - \sqrt 5 \\
&=& \sqrt{5} \cdot \sqrt{5} \cdot\sqrt{5}-\sqrt 5  \\
&=& \sqrt{5} (\sqrt{5} \cdot\sqrt{5} - 1)  \\
&=& \sqrt{5} (5 - 1)  \\
&=& 4 \sqrt{5}
\end{eqnarray}
$$

If the question were $\sqrt{125} \div \sqrt5$, then the answer would indeed be $5$.
