%5E1%2F2-radical-form.jpeg "(25x)^1/2 Radical Form")
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.