5/2sqrt{7-2sqrt{5}} eching

$$\frac { 5 } { 2 \sqrt { 7 } - 2 \sqrt { 5 } }$$

Baholash

$$\frac{5\left(\sqrt{5}+\sqrt{7}\right)}{4}\approx 6,102274111$$

Yechim qadamlari

\frac{5}{2\sqrt{7}-2\sqrt{5}} maxrajini 2\sqrt{7}+2\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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

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

\left(2\sqrt{7}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\left(\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

\sqrt{7} kvadrati – 7.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\times 7-\left(-2\sqrt{5}\right)^{2}}$$

28 hosil qilish uchun 4 va 7 ni ko'paytirish.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\sqrt{5}\right)^{2}}$$

\left(-2\sqrt{5}\right)^{2} ni kengaytirish.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\times 5}$$

20 hosil qilish uchun 4 va 5 ni ko'paytirish.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-20}$$

8 olish uchun 28 dan 20 ni ayirish.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{8}$$

5 ga 2\sqrt{7}+2\sqrt{5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{10\sqrt{7}+10\sqrt{5}}{8}$$