20/sqrt{6-sqrt{2}} eching

$$\frac{ 20 }{ \sqrt{ 6 } - \sqrt{ 2 } }$$

Baholash

$$5\left(\sqrt{2}+\sqrt{6}\right)\approx 19,318516526$$

Yechim qadamlari

\frac{20}{\sqrt{6}-\sqrt{2}} maxrajini \sqrt{6}+\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}+\sqrt{2}\right)}$$

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

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{6} kvadratini chiqarish. \sqrt{2} kvadratini chiqarish.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{6-2}$$

4 olish uchun 6 dan 2 ni ayirish.

$$\frac{20\left(\sqrt{6}+\sqrt{2}\right)}{4}$$

5\left(\sqrt{6}+\sqrt{2}\right) ni olish uchun 20\left(\sqrt{6}+\sqrt{2}\right) ni 4 ga bo‘ling.

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

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

$$5\sqrt{6}+5\sqrt{2}$$