frac{2sqrt{5}}{3+sqrt{3}} eching

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

Baholash

$$-\frac{\sqrt{15}}{3}+\sqrt{5}\approx 0,945073529$$

Yechim qadamlari

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

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

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}.

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

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

$$\frac{2\sqrt{5}\left(3-\sqrt{3}\right)}{9-3}$$

6 olish uchun 9 dan 3 ni ayirish.

$$\frac{2\sqrt{5}\left(3-\sqrt{3}\right)}{6}$$

2\sqrt{5} ga 3-\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{6\sqrt{5}-2\sqrt{3}\sqrt{5}}{6}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{6\sqrt{5}-2\sqrt{15}}{6}$$