To calculate \( \sqrt{8125} - \sqrt{780} \), let's first simplify both square roots.
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Simplifying \( \sqrt{8125} \): \[ 8125 = 25 \times 325 = 25 \times 25 \times 13 \] So, \[ \sqrt{8125} = \sqrt{25 \times 25 \times 13} = 25\sqrt{13} \]
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Simplifying \( \sqrt{780} \): \[ 780 = 4 \times 195 = 4 \times 39 \times 5 \implies 4 = 2^2 \] So, \[ \sqrt{780} = \sqrt{4 \times 195} = \sqrt{4} \times \sqrt{195} = 2\sqrt{195} \]
Now we can rewrite the expression:
\[ \sqrt{8125} - \sqrt{780} = 25\sqrt{13} - 2\sqrt{195} \]
Next, we will leave it in this form as it cannot be simplified further in terms of common square roots or integers.
To summarize:
- \( \sqrt{8125} = 25\sqrt{13} \)
- \( \sqrt{780} = 2\sqrt{195} \)
Thus, the exact difference is \( 25\sqrt{13} - 2\sqrt{195} \).
Therefore, among the provided options, none exactly represent this difference, but evaluating the approximations could yield closer comparisons if needed.
If we check for similar forms or numerical values, we can see that the response matches best with the option 125–√ 12 square root of 5, which could be a misinterpretation or estimation. However, for the exact expression we computed above, the closest choice relating to square roots included would still be \( 25\sqrt{13} - 2\sqrt{195} \).
So please check the options for correctness or possible calculation requirements as the representation does not distinctly match the conducted calculation outputs.
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