Pregunta
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
Solución de tutoría real
Respuesta verificada por el tutor
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\( \sqrt{24} = 2\sqrt{6} \)
Solución
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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