Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 10 \sqrt{5} \)
Solution
To simplify the expression \( 2 \sqrt{125} \), follow these steps:
1. **Factor the number inside the square root:**
\( 125 \) can be factored into \( 25 \times 5 \).
2. **Apply the property of square roots:**
\( \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} \).
3. **Simplify the square root of 25:**
\( \sqrt{25} = 5 \).
4. **Combine the results:**
\( \sqrt{125} = 5 \sqrt{5} \).
5. **Multiply by 2:**
\( 2 \sqrt{125} = 2 \times 5 \sqrt{5} = 10 \sqrt{5} \).
**Final Simplified Form:**
\[ 10 \sqrt{5} \]
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Simplify this solution Beyond the Answer
To simplify \( 2 \sqrt{125} \), start by breaking down 125 into its prime factors. We can express 125 as \( 25 \times 5 \) or \( 5^3 \). Recognizing that the square root of 25 is 5, we get: \[ \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} \] Now, substituting this back into the original expression gives: \[ 2 \sqrt{125} = 2 \times 5\sqrt{5} = 10\sqrt{5} \] Therefore, the simplified form of \( 2 \sqrt{125} \) is \[ 10\sqrt{5} \]
