Question
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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. \( \sqrt{24} = 2\sqrt{6} \)**

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Bonus Knowledge

A. \( \sqrt{24} = 2\sqrt{6} \) To simplify \( \sqrt{24} \), we can factor it into \( \sqrt{4 \times 6} \), which simplifies to \( \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \).

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