Question

Simplify the radical expression. $$\frac{1}{2} \sqrt{28}$$

Short answer

So, the simplified form of the given radical expression \( \frac{1}{2} \sqrt{28} \) is \( \sqrt{7} \).

Step-by-step solution

Perform Prime Factorization of the Number Under the Root

We begin with the prime factorization of 28, which is 2 * 2 * 7.

Use the Property of Radicals to Separate Them

Using the property that the square root of a product equals the product of square roots, we can now separate the numbers under the root. Thus, we get \( \frac{1}{2} \sqrt{2*2*7} \) = \( \frac{1}{2} \sqrt{2*2} \) * \( \sqrt{7} \)

Simplify the Expression

Squares under roots can be taken out as they are. We know that \( \sqrt{2*2} \) gives us 2. So we have \( \frac{1}{2} \) * 2* \( \sqrt{7} \), simplifying this gives us \( \sqrt{7} \).