frac{2sqrt{3}-sqrt{2}}{2sqrt{3}+sqrt{3}} eching

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

Baholash

$$-\frac{\sqrt{6}}{9}+\frac{2}{3}\approx 0,39450114$$

Yechim qadamlari

3\sqrt{3} ni olish uchun 2\sqrt{3} va \sqrt{3} ni birlashtirish.

$$\frac{2\sqrt{3}-\sqrt{2}}{3\sqrt{3}}$$

\frac{2\sqrt{3}-\sqrt{2}}{3\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

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

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

$$\frac{\left(2\sqrt{3}-\sqrt{2}\right)\sqrt{3}}{9}$$

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

$$\frac{2\left(\sqrt{3}\right)^{2}-\sqrt{2}\sqrt{3}}{9}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\times 3-\sqrt{2}\sqrt{3}}{9}$$

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

$$\frac{6-\sqrt{2}\sqrt{3}}{9}$$

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

$$\frac{6-\sqrt{6}}{9}$$

Omil

$$\frac{\sqrt{6} {(\sqrt{6} - 1)}}{9} = 0,3945011396907579$$