Solve sqrt{-18}*sqrt{-10}

$$\sqrt { - 18 } \cdot \sqrt { - 10 }$$

Evaluate (complex solution)

$$-6\sqrt{5}\approx -13.416407865$$

Solution Steps

Factor -18=\left(3i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 2} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{2}. Take the square root of \left(3i\right)^{2}.

$$3i\sqrt{2}\sqrt{-10}$$

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.

$$3i\sqrt{2}\sqrt{10}i$$

Multiply 3i and i to get -3.

$$-3\sqrt{2}\sqrt{10}$$

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}.

$$-3\sqrt{2}\sqrt{2}\sqrt{5}$$

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

$$-3\times 2\sqrt{5}$$

Multiply -3 and 2 to get -6.

$$-6\sqrt{5}$$

Real Part (complex solution)

$$-6\sqrt{5}$$

Evaluate

$$\text{Indeterminate}$$