frac{2sqrt{2}}{5-2sqrt{6}} eching

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

Baholash

$$8\sqrt{3}+10\sqrt{2}\approx 27,998542084$$

Yechim qadamlari

\frac{2\sqrt{2}}{5-2\sqrt{6}} maxrajini 5+2\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)}$$

Hisoblang: \left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{5^{2}-\left(-2\sqrt{6}\right)^{2}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}}$$

\left(-2\sqrt{6}\right)^{2} ni kengaytirish.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\times 6}$$

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-24}$$

1 olish uchun 25 dan 24 ni ayirish.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$2\sqrt{2}\left(5+2\sqrt{6}\right)$$

2\sqrt{2} ga 5+2\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10\sqrt{2}+4\sqrt{2}\sqrt{6}$$

Faktor: 6=2\times 3. \sqrt{2\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$10\sqrt{2}+4\times 2\sqrt{3}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$10\sqrt{2}+8\sqrt{3}$$