frac{4+3sqrt{2}}{2+sqrt{3}} eching

$$\frac { 4 + 3 \sqrt { 2 } } { 2 + \sqrt { 3 } }$$

Baholash

$$6\sqrt{2}+8-3\sqrt{6}-4\sqrt{3}\approx 2,208608916$$

Yechim qadamlari

\frac{4+3\sqrt{2}}{2+\sqrt{3}} maxrajini 2-\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(4+3\sqrt{2}\right)\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}$$

Hisoblang: \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(4+3\sqrt{2}\right)\left(2-\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}$$

2 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{\left(4+3\sqrt{2}\right)\left(2-\sqrt{3}\right)}{4-3}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{\left(4+3\sqrt{2}\right)\left(2-\sqrt{3}\right)}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$\left(4+3\sqrt{2}\right)\left(2-\sqrt{3}\right)$$

4+3\sqrt{2} ifodaning har bir elementini 2-\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$8-4\sqrt{3}+6\sqrt{2}-3\sqrt{3}\sqrt{2}$$

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

$$8-4\sqrt{3}+6\sqrt{2}-3\sqrt{6}$$