How do you find a square root of a fraction?

To find the square root of a fraction, follow these steps:

1. **Understand the problem**: A fraction is a number written in the form `a/b`, where `a` is the numerator and `b` is the denominator. The square root of the fraction is denoted as `√(a/b)`.

2. **Separate the square root**: Use the property of square roots that allows you to separate the numerator and denominator:
- `√(a/b) = √a / √b`

3. **Simplify each part**:
- Find the square root of the numerator `a` and the square root of the denominator `b`.
- If either `a` or `b` is a perfect square (e.g., 4, 9, 16), simplify its square root directly.
- If `a` or `b` is not a perfect square, you can leave the square root in its simplified radical form or approximate its value as a decimal.

4. **Rationalize the denominator if needed**:
- If the denominator contains a square root, you might need to "rationalize" it by multiplying the numerator and denominator by a value that eliminates the square root from the denominator.

### Example:
Find the square root of `4/9`.

1. Separate the square root:
- `√(4/9) = √4 / √9`

2. Simplify each part:
- `√4 = 2` and `√9 = 3`
- So, `√(4/9) = 2/3`

### Example with a non-perfect square:
Find the square root of `5/8`.

1. Separate the square root:
- `√(5/8) = √5 / √8`

2. Simplify the denominator:
- `√8 = √(4 × 2) = 2√2`
- So, `√(5/8) = √5 / (2√2)`

3. Rationalize the denominator:
- Multiply numerator and denominator by `√2`:
- `(√5 × √2) / (2√2 × √2) = √(10) / 4`

4. Final answer:
- `√(5/8) = √10 / 4`

By following these steps, you can find the square root of any fraction, whether the numbers are perfect squares or not.