sqrt{8}div(sqrt{2}-1) eching

$$\sqrt { 8 } \div ( \sqrt { 2 } - 1 )$$

Baholash

$$2\sqrt{2}+4\approx 6,828427125$$

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.

$$\frac{2\sqrt{2}}{\sqrt{2}-1}$$

\frac{2\sqrt{2}}{\sqrt{2}-1} maxrajini \sqrt{2}+1 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\sqrt{2}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}\right)^{2}-1^{2}}$$

\sqrt{2} kvadratini chiqarish. 1 kvadratini chiqarish.

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

1 olish uchun 2 dan 1 ni ayirish.

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

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

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

2\sqrt{2} ga \sqrt{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\sqrt{2} kvadrati – 2.

$$2\times 2+2\sqrt{2}$$

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

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