frac{sqrt{3}-5}{sqrt{7}+5} eching

$$\frac { \sqrt { 3 } - 5 } { \sqrt { 7 } + 5 }$$

Baholash

$$\frac{5\sqrt{3}+5\sqrt{7}-\sqrt{21}-25}{18}\approx -0,427420283$$

Yechim qadamlari

\frac{\sqrt{3}-5}{\sqrt{7}+5} maxrajini \sqrt{7}-5 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)}$$

Hisoblang: \left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{\left(\sqrt{7}\right)^{2}-5^{2}}$$

\sqrt{7} kvadratini chiqarish. 5 kvadratini chiqarish.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{7-25}$$

-18 olish uchun 7 dan 25 ni ayirish.

$$\frac{\left(\sqrt{3}-5\right)\left(\sqrt{7}-5\right)}{-18}$$

\sqrt{3}-5 ifodaning har bir elementini \sqrt{7}-5 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\sqrt{3}\sqrt{7}-5\sqrt{3}-5\sqrt{7}+25}{-18}$$

\sqrt{3} va \sqrt{7} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{21}-5\sqrt{3}-5\sqrt{7}+25}{-18}$$

Surat va maxrajini -1 ga ko‘paytiring.

$$\frac{-\sqrt{21}+5\sqrt{3}+5\sqrt{7}-25}{18}$$