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

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

Arvuta (complex solution)

$$20\sqrt{2}i\approx 28,284271247i$$

Lahenduse etapid

Tegurda -50=\left(5i\right)^{2}\times 2. Kirjutage \sqrt{\left(5i\right)^{2}\times 2} toote juured, kui see ruut \sqrt{\left(5i\right)^{2}}\sqrt{2}. Leidke \left(5i\right)^{2} ruutjuur.

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

Korrutage 5 ja 5i, et leida 25i.

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

Tegurda -18=\left(3i\right)^{2}\times 2. Kirjutage \sqrt{\left(3i\right)^{2}\times 2} toote juured, kui see ruut \sqrt{\left(3i\right)^{2}}\sqrt{2}. Leidke \left(3i\right)^{2} ruutjuur.

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

Korrutage -3 ja 3i, et leida -9i.

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

Kombineerige 25i\sqrt{2} ja -9i\sqrt{2}, et leida 16i\sqrt{2}.

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

Tegurda -8=\left(2i\right)^{2}\times 2. Kirjutage \sqrt{\left(2i\right)^{2}\times 2} toote juured, kui see ruut \sqrt{\left(2i\right)^{2}}\sqrt{2}. Leidke \left(2i\right)^{2} ruutjuur.

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

Korrutage 2 ja 2i, et leida 4i.

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

Kombineerige 16i\sqrt{2} ja 4i\sqrt{2}, et leida 20i\sqrt{2}.

$$20i\sqrt{2}$$

Reaalosa (complex solution)

$$0$$

Arvuta

$$\text{Indeterminate}$$