(2sqrt{3}+6sqrt{2})*sqrt{1/3} eching

$$(2 \sqrt{ 3 } +6 \sqrt{ 2 } ) \times \sqrt{ \frac{ 1 }{ 3 } }$$

Baholash

$$2\left(\sqrt{6}+1\right)\approx 6,898979486$$

Yechim qadamlari

\sqrt{\frac{1}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\left(2\sqrt{3}+6\sqrt{2}\right)\times \frac{\sqrt{1}}{\sqrt{3}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$\left(2\sqrt{3}+6\sqrt{2}\right)\times \frac{1}{\sqrt{3}}$$

\frac{1}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(2\sqrt{3}+6\sqrt{2}\right)\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\left(2\sqrt{3}+6\sqrt{2}\right)\times \frac{\sqrt{3}}{3}$$

\left(2\sqrt{3}+6\sqrt{2}\right)\times \frac{\sqrt{3}}{3} ni yagona kasrga aylantiring.

$$\frac{\left(2\sqrt{3}+6\sqrt{2}\right)\sqrt{3}}{3}$$

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

$$\frac{2\left(\sqrt{3}\right)^{2}+6\sqrt{2}\sqrt{3}}{3}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\times 3+6\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{6+6\sqrt{2}\sqrt{3}}{3}$$

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{6+6\sqrt{6}}{3}$$

Omil

$$2 {(\sqrt{6} + 1)} = 6,898979486$$