Evaluate (-32+ square root of 512)/-32

Problem

(−32+√(,512))/(−32)

Solution

1. Simplify the square root by finding the largest perfect square factor of 512

512=256⋅2

2. Extract the square root of the perfect square.

√(,512)=√(,256⋅2)

√(,512)=16√(,2)

3. Substitute the simplified radical back into the original expression.

(−32+16√(,2))/(−32)

4. Split the fraction into two separate terms to simplify.

(−32)/(−32)+(16√(,2))/(−32)

5. Reduce each term by dividing the coefficients.

1−√(,2)/2

Final Answer

(−32+√(,512))/(−32)=1−√(,2)/2

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