Problem 71 - 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: Prime Factorize the Number

Start by finding the prime factors of the number under the radical. This is done by dividing the number by prime numbers until only prime numbers are left. For the number 24, we find the prime factorization as \(2^3 \cdot 3^1\).

Step 2: Pairing the Factors

In the second step, pairs of the same factors are made. From the prime factorization, we find one pair of 2's: \((2,2)\) and one lone 2 and 3.

Step 3: Simplifying the radical

Each pair of identical factors corresponds to one factor in the simplified radical. From the paired 2's, we get a single two outside the radical. The lone factors stay under the radical. This gives us the final answer: \(2\sqrt{6}\).