Solve sqrt{-10}*sqrt{-80}

$$\sqrt { - 10 } \times \sqrt { - 80 }$$

Evaluate (complex solution)

$$-20\sqrt{2}\approx -28.284271247$$

Solution Steps

Factor -10=10\left(-1\right). Rewrite the square root of the product \sqrt{10\left(-1\right)} as the product of square roots \sqrt{10}\sqrt{-1}. By definition, the square root of -1 is i.

$$\sqrt{10}i\sqrt{-80}$$

Factor -80=\left(4i\right)^{2}\times 5. Rewrite the square root of the product \sqrt{\left(4i\right)^{2}\times 5} as the product of square roots \sqrt{\left(4i\right)^{2}}\sqrt{5}. Take the square root of \left(4i\right)^{2}.

$$\sqrt{10}i\times \left(4i\right)\sqrt{5}$$

Multiply i and 4i to get -4.

$$\sqrt{10}\left(-4\right)\sqrt{5}$$

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

$$\sqrt{5}\sqrt{2}\left(-4\right)\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\left(-4\right)\sqrt{2}$$

Multiply 5 and -4 to get -20.

$$-20\sqrt{2}$$

Real Part (complex solution)

$$-20\sqrt{2}$$

Evaluate

$$\text{Indeterminate}$$