Solve (sqrt{-4}-sqrt{6})*sqrt{24}

$$( \sqrt { - 4 } - \sqrt { 6 } ) \times \sqrt { 24 }$$

Evaluate (complex solution)

$$-12+4\sqrt{6}i\approx -12+9.797958971i$$

Solution Steps

Calculate the square root of -4 and get 2i.

$$\left(2i-\sqrt{6}\right)\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\left(2i-\sqrt{6}\right)\times 2\sqrt{6}$$

Use the distributive property to multiply 2i-\sqrt{6} by 2.

$$\left(4i-2\sqrt{6}\right)\sqrt{6}$$

Use the distributive property to multiply 4i-2\sqrt{6} by \sqrt{6}.

$$4i\sqrt{6}-2\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$4i\sqrt{6}-2\times 6$$

Multiply -2 and 6 to get -12.

$$4i\sqrt{6}-12$$

Real Part (complex solution)

$$-12$$

Evaluate

$$\text{Indeterminate}$$