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

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

Baholash

$$\frac{\sqrt{6}+\sqrt{15}}{3}\approx 2,10749103$$

Yechim qadamlari

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

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

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

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

\sqrt{5} kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

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

3 olish uchun 5 dan 2 ni ayirish.

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

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

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

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

$$\frac{\sqrt{15}+\sqrt{3}\sqrt{2}}{3}$$

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

$$\frac{\sqrt{15}+\sqrt{6}}{3}$$