Question

Simplify the radical expression. $$ \sqrt{24} $$

Short answer

The simplified form of the radical expression \(\sqrt{24}\) is \(2\sqrt{6}\).

Step-by-step solution

Prime Factorization of 24

Start the simplification process by breaking down the number under the square root, 24, into its prime factors. The prime factorization of 24 is \(2 \times 2 \times 2 \times 3\), or \(2^3 \times 3^1\).

Pair up the factors

For a square root, every pair of similar factors can be moved out of the root. Since there are three 2's, two of them can pair up and move outside of the root. The one unpaired 2 and 3 remain under the root.

Simplifying the radical expression

By moving the pair of 2’s outside the root, the simplified radical expression becomes \(2\sqrt{6}\).