Solve frac{-2+sqrt{4^2-4}}{2}

$$\frac{ -2+ \sqrt{ { 4 }^{ 2 } -4 } }{ 2 }$$

Evaluate

$$\sqrt{3}-1\approx 0.732050808$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-2+\sqrt{16-4}}{2}$$

Subtract 4 from 16 to get 12.

$$\frac{-2+\sqrt{12}}{2}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{-2+2\sqrt{3}}{2}$$

Divide each term of -2+2\sqrt{3} by 2 to get -1+\sqrt{3}.

$$-1+\sqrt{3}$$

Factor

$$\sqrt{3} - 1 = 0.732050808$$