=frac{12sqrt{3}+24}{sqrt{2}+sqrt{6}} eching

$$= \frac { 12 \sqrt { 3 } + 24 } { \sqrt { 2 } + \sqrt { 6 } }$$

Baholash

$$3\left(\sqrt{2}+\sqrt{6}\right)\approx 11,591109915$$

Yechim qadamlari

\frac{12\sqrt{3}+24}{\sqrt{2}+\sqrt{6}} maxrajini \sqrt{2}-\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{6}\right)}$$

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

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{2-6}$$

-4 olish uchun 2 dan 6 ni ayirish.

$$\frac{\left(12\sqrt{3}+24\right)\left(\sqrt{2}-\sqrt{6}\right)}{-4}$$

12\sqrt{3}+24 ifodaning har bir elementini \sqrt{2}-\sqrt{6} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{12\sqrt{3}\sqrt{2}-12\sqrt{3}\sqrt{6}+24\sqrt{2}-24\sqrt{6}}{-4}$$

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

$$\frac{12\sqrt{6}-12\sqrt{3}\sqrt{6}+24\sqrt{2}-24\sqrt{6}}{-4}$$

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{12\sqrt{6}-12\sqrt{3}\sqrt{3}\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{12\sqrt{6}-12\times 3\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

-36 hosil qilish uchun -12 va 3 ni ko'paytirish.

$$\frac{12\sqrt{6}-36\sqrt{2}+24\sqrt{2}-24\sqrt{6}}{-4}$$

-12\sqrt{2} ni olish uchun -36\sqrt{2} va 24\sqrt{2} ni birlashtirish.

$$\frac{12\sqrt{6}-12\sqrt{2}-24\sqrt{6}}{-4}$$

-12\sqrt{6} ni olish uchun 12\sqrt{6} va -24\sqrt{6} ni birlashtirish.

$$\frac{-12\sqrt{6}-12\sqrt{2}}{-4}$$

Omil

$$3 {(\sqrt{2} + \sqrt{6})} = 11,591109915$$