Evaluate

Problem

√(,2)/4+√(,6)/4

Solution

1. Identify the common denominator. Both fractions have a denominator of 4

2. Combine the numerators over the single common denominator.

(√(,2)+√(,6))/4

3. Factor the numerator if possible. Since √(,6)=√(,2)⋅√(,3) we can factor out √(,2)

(√(,2)*(1+√(,3)))/4

4. Recognize the expression as a known trigonometric value. This expression is the exact value for sin(75) or cos(15) though the combined fraction is the standard simplified form.

Final Answer

√(,2)/4+√(,6)/4=(√(,2)+√(,6))/4

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