frac{6+sqrt{27}}{4-sqrt{3}} eching

$$\frac { 6 + \sqrt { 27 } } { 4 - \sqrt { 3 } }$$

Baholash

$$\frac{18\sqrt{3}+33}{13}\approx 4,936685734$$

Yechim qadamlari

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{6+3\sqrt{3}}{4-\sqrt{3}}$$

\frac{6+3\sqrt{3}}{4-\sqrt{3}} maxrajini 4+\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

4 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{\left(6+3\sqrt{3}\right)\left(4+\sqrt{3}\right)}{16-3}$$

13 olish uchun 16 dan 3 ni ayirish.

$$\frac{\left(6+3\sqrt{3}\right)\left(4+\sqrt{3}\right)}{13}$$

6+3\sqrt{3} ifodaning har bir elementini 4+\sqrt{3} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{24+6\sqrt{3}+12\sqrt{3}+3\left(\sqrt{3}\right)^{2}}{13}$$

18\sqrt{3} ni olish uchun 6\sqrt{3} va 12\sqrt{3} ni birlashtirish.

$$\frac{24+18\sqrt{3}+3\left(\sqrt{3}\right)^{2}}{13}$$

\sqrt{3} kvadrati – 3.

$$\frac{24+18\sqrt{3}+3\times 3}{13}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$\frac{24+18\sqrt{3}+9}{13}$$

33 olish uchun 24 va 9'ni qo'shing.

$$\frac{33+18\sqrt{3}}{13}$$