Solve (sqrt{-40})(sqrt{-2})

$$( \sqrt { - 40 } ) ( \sqrt { - 2 } )$$

Evaluate (complex solution)

$$-4\sqrt{5}\approx -8.94427191$$

Solution Steps

Factor -40=\left(2i\right)^{2}\times 10. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 10} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{10}. Take the square root of \left(2i\right)^{2}.

$$2i\sqrt{10}\sqrt{-2}$$

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

$$2i\sqrt{10}\sqrt{2}i$$

Multiply 2i and i to get -2.

$$-2\sqrt{10}\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$-2\sqrt{2}\sqrt{5}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$-2\times 2\sqrt{5}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{5}$$

Real Part (complex solution)

$$-4\sqrt{5}$$

Evaluate

$$\text{Indeterminate}$$