Solve -(4)divsqrt{(4)^2-4}*(2)

$$- ( 4 ) \div \sqrt { ( 4 ) ^ { 2 } - 4 } \cdot ( 2 )$$

Evaluate

$$-\frac{4\sqrt{3}}{3}\approx -2.309401077$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

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

Subtract 4 from 16 to get 12.

$$\frac{-4}{\sqrt{12}}\times 2$$

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}.

$$\frac{-4}{2\sqrt{3}}\times 2$$

Rationalize the denominator of \frac{-4}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-4\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\times 2$$

The square of \sqrt{3} is 3.

$$\frac{-4\sqrt{3}}{2\times 3}\times 2$$

Cancel out 2 in both numerator and denominator.

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

Express \frac{-2\sqrt{3}}{3}\times 2 as a single fraction.

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

Multiply -2 and 2 to get -4.

$$\frac{-4\sqrt{3}}{3}$$