# How do you simplify the 9 square root 125?

Mar 11, 2018

Radical form simplified: $45 \sqrt{5}$
Decimal form simplified: Around $100.62$

#### Explanation:

By 9 square root 125 I suppose you mean $9 \sqrt{125}$.

I'm not sure whether you want the simplified version to be in radical form or decimal form, but I'll show both.

To simplify this radical further, we have to see if the thing inside the sqrt has factors that are squarerootable (that's not a word). We know that $125$ is divisible by $25$, and $25$ can be square rooted to $5$. So $\sqrt{125} = \sqrt{5 \cdot 25} = 5 \sqrt{5}$.
Remember we still have the $9$ in front, meaning that it becomes:
$9 \cdot 5 \sqrt{5} = 45 \sqrt{5}$
First, we plug into the calculator $\sqrt{125}$ to find the value of that, which is about $11.18$. Then we multiply this by $9$ and get about $100.62$