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

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

Baholash

$$\frac{\sqrt{15}+\sqrt{35}+3\sqrt{3}+3\sqrt{7}}{4}\approx 5,730617371$$

Yechim qadamlari

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

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

Hisoblang: \left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\sqrt{7} kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

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

4 olish uchun 7 dan 3 ni ayirish.

$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{7}+\sqrt{3}\right)}{4}$$

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

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{5}\sqrt{7}+\sqrt{5}\sqrt{3}}{4}$$

\sqrt{5} va \sqrt{7} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{5}\sqrt{3}}{4}$$

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

$$\frac{3\sqrt{7}+3\sqrt{3}+\sqrt{35}+\sqrt{15}}{4}$$