frac{sqrt{18}-sqrt{12}}{sqrt{50}-sqrt{48}} eching

$$\frac { \sqrt { 18 } - \sqrt { 12 } } { \sqrt { 50 } - \sqrt { 48 } }$$

Baholash

$$\sqrt{6}+3\approx 5,449489743$$

Yechim qadamlari

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.

$$\frac{3\sqrt{2}-\sqrt{12}}{\sqrt{50}-\sqrt{48}}$$

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{50}-\sqrt{48}}$$

Faktor: 50=5^{2}\times 2. \sqrt{5^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$\frac{3\sqrt{2}-2\sqrt{3}}{5\sqrt{2}-\sqrt{48}}$$

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.

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

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

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

Hisoblang: \left(5\sqrt{2}-4\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(5\sqrt{2}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{25\left(\sqrt{2}\right)^{2}-\left(-4\sqrt{3}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{25\times 2-\left(-4\sqrt{3}\right)^{2}}$$

50 hosil qilish uchun 25 va 2 ni ko'paytirish.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{50-\left(-4\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{50-\left(-4\right)^{2}\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{50-16\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{50-16\times 3}$$

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

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}+4\sqrt{3}\right)}{50-48}$$

2 olish uchun 50 dan 48 ni ayirish.

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

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

$$\frac{15\left(\sqrt{2}\right)^{2}+12\sqrt{3}\sqrt{2}-10\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}}{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{15\times 2+12\sqrt{3}\sqrt{2}-10\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}}{2}$$

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

$$\frac{30+12\sqrt{3}\sqrt{2}-10\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}}{2}$$

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

$$\frac{30+12\sqrt{6}-10\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}}{2}$$

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

$$\frac{30+12\sqrt{6}-10\sqrt{6}-8\left(\sqrt{3}\right)^{2}}{2}$$

2\sqrt{6} ni olish uchun 12\sqrt{6} va -10\sqrt{6} ni birlashtirish.

$$\frac{30+2\sqrt{6}-8\left(\sqrt{3}\right)^{2}}{2}$$

\sqrt{3} kvadrati – 3.

$$\frac{30+2\sqrt{6}-8\times 3}{2}$$

-24 hosil qilish uchun -8 va 3 ni ko'paytirish.

$$\frac{30+2\sqrt{6}-24}{2}$$

6 olish uchun 30 dan 24 ni ayirish.

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

3+\sqrt{6} natijani olish uchun 6+2\sqrt{6} ning har bir ifodasini 2 ga bo‘ling.

$$3+\sqrt{6}$$