Question
Simplify the square root. Assume all variables represent positive numbers. If the square root is already simplified, so state. \( \sqrt{24} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sqrt{24}=\square \) (Type an exact answer, using radicals as needed.) B. The expression is already simplified.
Ask by Nichols Barnett. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{24} = 2\sqrt{6} \)
Solution
To simplify \( \sqrt{24} \), follow these steps:
1. **Factor the Number Inside the Square Root:**
\[
24 = 4 \times 6
\]
2. **Identify the Largest Perfect Square Factor:**
\[
4 \text{ is a perfect square since } \sqrt{4} = 2.
\]
3. **Simplify the Square Root:**
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
Since \( 2\sqrt{6} \) is the simplest form, the correct choice is:
**A. \( \sqrt{24} = 2\sqrt{6} \)**
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain
Simplify this solution
Bonus Knowledge
A. \( \sqrt{24} = 2\sqrt{6} \) To simplify \( \sqrt{24} \), we can factor it into \( \sqrt{4 \times 6} \), which simplifies to \( \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \).