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

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

Baholash

$$\frac{-\sqrt{6}-\sqrt{10}}{2}\approx -2,805883701$$

Yechim qadamlari

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

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

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

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

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

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

-2 olish uchun 3 dan 5 ni ayirish.

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

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

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

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

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

\sqrt{2} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{6}+\sqrt{10}}{-2}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-\sqrt{6}-\sqrt{10}}{2}$$