Solve 5sqrt{-50}-3sqrt{-18}+2sqrt{-8}

$$5 \sqrt { - 50 } - 3 \sqrt { - 18 } + 2 \sqrt { - 8 }$$

Evaluate (complex solution)

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

Solution Steps

Factor -50=\left(5i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 2} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{2}. Take the square root of \left(5i\right)^{2}.

$$5\times \left(5i\right)\sqrt{2}-3\sqrt{-18}+2\sqrt{-8}$$

Multiply 5 and 5i to get 25i.

$$25i\sqrt{2}-3\sqrt{-18}+2\sqrt{-8}$$

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}.

$$25i\sqrt{2}-3\times \left(3i\right)\sqrt{2}+2\sqrt{-8}$$

Multiply -3 and 3i to get -9i.

$$25i\sqrt{2}-9i\sqrt{2}+2\sqrt{-8}$$

Combine 25i\sqrt{2} and -9i\sqrt{2} to get 16i\sqrt{2}.

$$16i\sqrt{2}+2\sqrt{-8}$$

Factor -8=\left(2i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 2} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{2}. Take the square root of \left(2i\right)^{2}.

$$16i\sqrt{2}+2\times \left(2i\right)\sqrt{2}$$

Multiply 2 and 2i to get 4i.

$$16i\sqrt{2}+4i\sqrt{2}$$

Combine 16i\sqrt{2} and 4i\sqrt{2} to get 20i\sqrt{2}.

$$20i\sqrt{2}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$