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

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

Baholash (complex solution)

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

Yechim qadamlari

Faktor: -50=\left(5i\right)^{2}\times 2. \sqrt{\left(5i\right)^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{\left(5i\right)^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. \left(5i\right)^{2} ning kvadrat ildizini chiqarish.

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

25i hosil qilish uchun 5 va 5i ni ko'paytirish.

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

Faktor: -18=\left(3i\right)^{2}\times 2. \sqrt{\left(3i\right)^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{\left(3i\right)^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. \left(3i\right)^{2} ning kvadrat ildizini chiqarish.

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

-9i hosil qilish uchun -3 va 3i ni ko'paytirish.

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

16i\sqrt{2} ni olish uchun 25i\sqrt{2} va -9i\sqrt{2} ni birlashtirish.

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

Faktor: -8=\left(2i\right)^{2}\times 2. \sqrt{\left(2i\right)^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{\left(2i\right)^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. \left(2i\right)^{2} ning kvadrat ildizini chiqarish.

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

4i hosil qilish uchun 2 va 2i ni ko'paytirish.

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

20i\sqrt{2} ni olish uchun 16i\sqrt{2} va 4i\sqrt{2} ni birlashtirish.

$$20i\sqrt{2}$$

Ashyoviy qism (complex solution)

$$0$$

Baholash

$$\text{Indeterminate}$$