The problem asks us to find the square root of the fraction $\frac{625}{1296}$. That is, we need to evaluate $\sqrt{\frac{625}{1296}}$.

1. Problem Description

The problem asks us to find the square root of the fraction $\frac{625}{1296}$. That is, we need to evaluate $\sqrt{\frac{625}{1296}}$.

2. Solution Steps

We can simplify the expression by taking the square root of the numerator and the square root of the denominator separately.

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

First, we find the square root of

6

2

5. Since $25 \times 25 = 625$, we have $\sqrt{625} = 25$.

Next, we find the square root of

1

2

9

6. We can notice that $30^2 = 900$ and $40^2 = 1600$. So the square root should be between 30 and

4

0. Since the last digit of 1296 is 6, the last digit of the square root can be either 4 or

6. We can test $34^2 = 34 \times 34 = 1156$, and $36^2 = 36 \times 36 = 1296$.

So, $\sqrt{1296} = 36$.

Therefore,

$\sqrt{\frac{625}{1296}} = \frac{\sqrt{625}}{\sqrt{1296}} = \frac{25}{36}$

3. Final Answer

$\frac{25}{36}$