=frac{7sqrt{3}-5sqrt{2}}{sqrt{48}+sqrt{18}} eching

$$= \frac { 7 \sqrt { 3 } - 5 \sqrt { 2 } } { \sqrt { 48 } + \sqrt { 18 } }$$

Baholash

$$-\frac{41\sqrt{6}}{30}+\frac{19}{5}\approx 0,452364018$$

Yechim qadamlari

Faktor: 48=4^{2}\times 3. \sqrt{4^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+\sqrt{18}}$$

Faktor: 18=3^{2}\times 2. \sqrt{3^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$$

\frac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}} maxrajini 4\sqrt{3}-3\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{\left(4\sqrt{3}+3\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}$$

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

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{\left(4\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

\left(4\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{4^{2}\left(\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{16\left(\sqrt{3}\right)^{2}-\left(3\sqrt{2}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{16\times 3-\left(3\sqrt{2}\right)^{2}}$$

48 hosil qilish uchun 16 va 3 ni ko'paytirish.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-\left(3\sqrt{2}\right)^{2}}$$

\left(3\sqrt{2}\right)^{2} ni kengaytirish.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-3^{2}\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-9\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-9\times 2}$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{48-18}$$

30 olish uchun 48 dan 18 ni ayirish.

$$\frac{\left(7\sqrt{3}-5\sqrt{2}\right)\left(4\sqrt{3}-3\sqrt{2}\right)}{30}$$

7\sqrt{3}-5\sqrt{2} ifodaning har bir elementini 4\sqrt{3}-3\sqrt{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{28\left(\sqrt{3}\right)^{2}-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

\sqrt{3} kvadrati – 3.

$$\frac{28\times 3-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

84 hosil qilish uchun 28 va 3 ni ko'paytirish.

$$\frac{84-21\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

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

$$\frac{84-21\sqrt{6}-20\sqrt{3}\sqrt{2}+15\left(\sqrt{2}\right)^{2}}{30}$$

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

$$\frac{84-21\sqrt{6}-20\sqrt{6}+15\left(\sqrt{2}\right)^{2}}{30}$$

-41\sqrt{6} ni olish uchun -21\sqrt{6} va -20\sqrt{6} ni birlashtirish.

$$\frac{84-41\sqrt{6}+15\left(\sqrt{2}\right)^{2}}{30}$$

\sqrt{2} kvadrati – 2.

$$\frac{84-41\sqrt{6}+15\times 2}{30}$$

30 hosil qilish uchun 15 va 2 ni ko'paytirish.

$$\frac{84-41\sqrt{6}+30}{30}$$

114 olish uchun 84 va 30'ni qo'shing.

$$\frac{114-41\sqrt{6}}{30}$$