frac{sqrt{3}+sqrt{3}}{sqrt{2}-1} eching

$$\frac { \sqrt { 3 } + \sqrt { 3 } } { \sqrt { 2 } - 1 }$$

Baholash

$$2\sqrt{3}\left(\sqrt{2}+1\right)\approx 8,363081101$$

Yechim qadamlari

2\sqrt{3} ni olish uchun \sqrt{3} va \sqrt{3} ni birlashtirish.

$$\frac{2\sqrt{3}}{\sqrt{2}-1}$$

\frac{2\sqrt{3}}{\sqrt{2}-1} maxrajini \sqrt{2}+1 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{3}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}$$

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}.

$$\frac{2\sqrt{3}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}\right)^{2}-1^{2}}$$

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

$$\frac{2\sqrt{3}\left(\sqrt{2}+1\right)}{2-1}$$

1 olish uchun 2 dan 1 ni ayirish.

$$\frac{2\sqrt{3}\left(\sqrt{2}+1\right)}{1}$$

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

$$2\sqrt{3}\left(\sqrt{2}+1\right)$$

2\sqrt{3} ga \sqrt{2}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$2\sqrt{6}+2\sqrt{3}$$

Omil

$$2 \sqrt{3} {(\sqrt{2} + 1)} = 8,363081101$$