Problem 62 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

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

Step 1: Factor the radicand

Start by factoring the number under the root symbol. The number 24 can be factored into 4 and 6, where 4 is a perfect square. Therefore, \(\sqrt{24} = \sqrt{4 \cdot 6}\).

Step 2: Apply the rule of square roots

The square root of a product can be rewritten as the product of the square roots, according to the property \(\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}\) when both a and b are positive. So we can rewrite the expression as \(\sqrt{4} \cdot \sqrt{6}\).

Step 3: Simplify

Now simplify where possible: \(\sqrt{4} = 2\), and \(\sqrt{6}\) can't be further simplified. So our final result is \(2\sqrt{6}\).