3/3-sqrt{3} eching

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

Baholash

$$\frac{\sqrt{3}+3}{2}\approx 2,366025404$$

Yechim qadamlari

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

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

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

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

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

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

6 olish uchun 9 dan 3 ni ayirish.

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

\frac{1}{2}\left(3+\sqrt{3}\right) ni olish uchun 3\left(3+\sqrt{3}\right) ni 6 ga bo‘ling.

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

\frac{1}{2} ga 3+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{2}\times 3+\frac{1}{2}\sqrt{3}$$

\frac{3}{2} hosil qilish uchun \frac{1}{2} va 3 ni ko'paytirish.

$$\frac{3}{2}+\frac{1}{2}\sqrt{3}$$