(2sqrt{-5}+3sqrt{-2})(-3sqrt{-8}) eching

$$( 2 \sqrt { - 5 } + 3 \sqrt { - 2 } ) ( - 3 \sqrt { - 8 } )$$

Baholash (complex solution)

$$12\left(\sqrt{10}+3\right)\approx 73,947331922$$

Yechim qadamlari

Faktor: -5=5\left(-1\right). \sqrt{5\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{5}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

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

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

Faktor: -2=2\left(-1\right). \sqrt{2\left(-1\right)} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{-1} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. Ta’rifi bo‘yicha, -1 ning kvadrat ildizi i ga teng.

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

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

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

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.

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

-6i hosil qilish uchun -3 va 2i ni ko'paytirish.

$$\left(2i\sqrt{5}+3i\sqrt{2}\right)\times \left(-6i\right)\sqrt{2}$$

2i\sqrt{5}+3i\sqrt{2} ga -6i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(12\sqrt{5}+18\sqrt{2}\right)\sqrt{2}$$

12\sqrt{5}+18\sqrt{2} ga \sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12\sqrt{5}\sqrt{2}+18\left(\sqrt{2}\right)^{2}$$

\sqrt{5} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$12\sqrt{10}+18\left(\sqrt{2}\right)^{2}$$

\sqrt{2} kvadrati – 2.

$$12\sqrt{10}+18\times 2$$

36 hosil qilish uchun 18 va 2 ni ko'paytirish.

$$12\sqrt{10}+36$$

Ashyoviy qism (complex solution)

$$12 {(\sqrt{10} + 3)} = 73,947331922$$

Baholash

$$\text{Indeterminate}$$