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

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

Baholash

$$-\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{4}\approx 0,270090757$$

Yechim qadamlari

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

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

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

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

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

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

-4 olish uchun 5 dan 9 ni ayirish.

$$\frac{\sqrt{2}\left(\sqrt{5}-3\right)}{-4}$$

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

$$\frac{\sqrt{2}\sqrt{5}-3\sqrt{2}}{-4}$$

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

$$\frac{\sqrt{10}-3\sqrt{2}}{-4}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-\sqrt{10}+3\sqrt{2}}{4}$$