8/sqrt{4-sqrt{2}} eching

$$\frac{ 8 }{ \sqrt{ 4 } - \sqrt{ 2 } }$$

Baholash

$$4\sqrt{2}+8\approx 13,656854249$$

Yechim qadamlari

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$\frac{8}{2-\sqrt{2}}$$

\frac{8}{2-\sqrt{2}} maxrajini 2+\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

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

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

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

$$\frac{8\left(2+\sqrt{2}\right)}{4-2}$$

2 olish uchun 4 dan 2 ni ayirish.

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

4\left(2+\sqrt{2}\right) ni olish uchun 8\left(2+\sqrt{2}\right) ni 2 ga bo‘ling.

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

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

$$8+4\sqrt{2}$$