## Simplifying Radicals: Understanding (25x)^1/2

The expression **(25x)^1/2** represents the square root of 25x. Let's break down how to simplify this radical expression.

### Understanding Fractional Exponents

The exponent 1/2 is a fractional exponent, indicating a **root**. Specifically, a fractional exponent of 1/n means taking the nth root of the base. In our case, 1/2 signifies the square root.

### Simplifying the Radical

**Separate the terms:**We can rewrite (25x)^1/2 as (25)^1/2 * (x)^1/2**Simplify each term:**- (25)^1/2 = 5 (The square root of 25 is 5)
- (x)^1/2 = √x (This cannot be simplified further)

**Combine the simplified terms:**5 * √x =**5√x**

Therefore, the simplified radical form of (25x)^1/2 is **5√x**.

### Key Points to Remember

**Fractional exponents represent roots.**1/2 is a square root, 1/3 is a cube root, and so on.**You can simplify radicals by factoring out perfect squares.**In our example, 25 is a perfect square, allowing us to simplify the radical.

By understanding these concepts, you can effectively simplify radical expressions involving fractional exponents.