To find which expression is equivalent to \( 10\sqrt{5} \), we can simplify each option and see if any equal \( 10\sqrt{5} \).
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Option A: \( \sqrt{500} \) \[ \sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5} \]
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Option B: \( \sqrt{105} \)
- Cannot be simplified further to match \( 10\sqrt{5} \).
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Option C: \( \sqrt{50} \) \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]
- This does not equal \( 10\sqrt{5} \).
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Option D: \( \sqrt{15} \)
- This does not simplify to match \( 10\sqrt{5} \).
Based on the calculations, the only expression that is equivalent to \( 10\sqrt{5} \) is:
A. \( \sqrt{500} \).