1/2sqrt{48}div(3sqrt{2}-sqrt{3}) eching

$$\frac { 1 } { 2 } \sqrt { 48 } \div ( 3 \sqrt { 2 } - \sqrt { 3 } )$$

Baholash

$$\frac{2\left(\sqrt{6}+1\right)}{5}\approx 1,379795897$$

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.

$$\frac{\frac{1}{2}\times 4\sqrt{3}}{3\sqrt{2}-\sqrt{3}}$$

\frac{4}{2} hosil qilish uchun \frac{1}{2} va 4 ni ko'paytirish.

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

2 ni olish uchun 4 ni 2 ga bo‘ling.

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

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

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

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

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

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

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

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

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{9\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{9\times 2-\left(\sqrt{3}\right)^{2}}$$

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

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

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{18-3}$$

15 olish uchun 18 dan 3 ni ayirish.

$$\frac{2\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)}{15}$$

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

$$\frac{6\sqrt{3}\sqrt{2}+2\left(\sqrt{3}\right)^{2}}{15}$$

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

$$\frac{6\sqrt{6}+2\left(\sqrt{3}\right)^{2}}{15}$$

\sqrt{3} kvadrati – 3.

$$\frac{6\sqrt{6}+2\times 3}{15}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{6\sqrt{6}+6}{15}$$