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2+\sqrt{6}-\sqrt{\frac{1}{4}}
Calculate \sqrt[3]{8} and get 2.
2+\sqrt{6}-\frac{1}{2}
Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.
\frac{3}{2}+\sqrt{6}
Subtract \frac{1}{2} from 2 to get \frac{3}{2}.