Question

Simplify each square root.

$\sqrt{\frac{25}{324}}$

Short answer

The square root of the number is$\frac{5}{18}$.

Step-by-step solution

Step 1. Identify the perfect square.

We know that $25=5^2$ and $324={18}^2$.

Step 2. The square root of the perfect square.

Since $25=5^2$ and $324={18}^2$. So, we can write$\sqrt{\frac{25}{324}}=\sqrt{\frac{5^2}{{18}^2}}=\sqrt{{\left(\frac{5}{18}\right)}^2}$

Step 3. Cancel square and square root.

$\sqrt{{\left(\frac{5}{18}\right)}^2}=\frac{5}{18}$