Evaluate square root of (1-(-8/17))/2

Problem

√(,(1−(−8/17))/2)

Solution

1. Simplify the numerator inside the square root by handling the double negative.

(1−(−8/17))/2=(1+8/17)/2

2. Combine the terms in the numerator by finding a common denominator.

1+8/17=17/17+8/17

17/17+8/17=25/17

3. Divide the resulting fraction by 2.

25/17/2=25/17⋅1/2

25/17⋅1/2=25/34

4. Apply the square root to the fraction.

√(,25/34)=√(,25)/√(,34)

5. Evaluate the square root of the numerator.

√(,25)/√(,34)=5/√(,34)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,34)

5/√(,34)⋅√(,34)/√(,34)=(5√(,34))/34

Final Answer

√(,(1−(−8/17))/2)=(5√(,34))/34

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