Evaluate ( square root of 25(100-25))/1250

Problem

√(,25*(100−25))/1250

Solution

1. Simplify the expression inside the parentheses.

100−25=75

2. Multiply the terms inside the square root.

25⋅75=1875

3. Simplify the square root by factoring out perfect squares.

√(,1875)=√(,625⋅3)

4. Evaluate the square root of the perfect square.

√(,625⋅3)=25√(,3)

5. Substitute the simplified radical back into the fraction.

(25√(,3))/1250

6. Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor, 25.

25/1250=1/50

Final Answer

√(,25*(100−25))/1250=√(,3)/50

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