Evaluate
50\sqrt{5}\approx 111.803398875
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0.25\sqrt{400000-200000}
Add 300000 and 100000 to get 400000.
0.25\sqrt{200000}
Subtract 200000 from 400000 to get 200000.
0.25\times 200\sqrt{5}
Factor 200000=200^{2}\times 5. Rewrite the square root of the product \sqrt{200^{2}\times 5} as the product of square roots \sqrt{200^{2}}\sqrt{5}. Take the square root of 200^{2}.
50\sqrt{5}
Multiply 0.25 and 200 to get 50.
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