2/5-sqrt{3} eching

$$\frac{ 2 }{ 5- \sqrt{ 3 } }$$

Baholash

$$\frac{\sqrt{3}+5}{11}\approx 0,612004619$$

Yechim qadamlari

\frac{2}{5-\sqrt{3}} maxrajini 5+\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(5+\sqrt{3}\right)}{5^{2}-\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{2\left(5+\sqrt{3}\right)}{25-3}$$

22 olish uchun 25 dan 3 ni ayirish.

$$\frac{2\left(5+\sqrt{3}\right)}{22}$$

\frac{1}{11}\left(5+\sqrt{3}\right) ni olish uchun 2\left(5+\sqrt{3}\right) ni 22 ga bo‘ling.

$$\frac{1}{11}\left(5+\sqrt{3}\right)$$

\frac{1}{11} ga 5+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{11}\times 5+\frac{1}{11}\sqrt{3}$$

\frac{5}{11} hosil qilish uchun \frac{1}{11} va 5 ni ko'paytirish.

$$\frac{5}{11}+\frac{1}{11}\sqrt{3}$$