5/sqrt{6-sqrt{8}} eching

$$\frac{ 5 }{ \sqrt{ 6 } - \sqrt{ 8 } }$$

Baholash

$$-\frac{5\sqrt{6}}{2}-5\sqrt{2}\approx -13,194792169$$

Yechim qadamlari

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

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

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

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

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

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

\sqrt{6} kvadrati – 6.

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

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

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

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

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

\sqrt{2} kvadrati – 2.

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

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

$$\frac{5\left(\sqrt{6}+2\sqrt{2}\right)}{6-8}$$

-2 olish uchun 6 dan 8 ni ayirish.

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

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

$$\frac{5\sqrt{6}+10\sqrt{2}}{-2}$$