frac{2sqrt{3}}{7+sqrt{6}} eching

$$\frac { 2 \sqrt { 3 } } { 7 + \sqrt { 6 } }$$

Baholash

$$\frac{14\sqrt{3}-6\sqrt{2}}{43}\approx 0,366591394$$

Yechim qadamlari

\frac{2\sqrt{3}}{7+\sqrt{6}} maxrajini 7-\sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{\left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right)}$$

Hisoblang: \left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}$$

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

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{49-6}$$

43 olish uchun 49 dan 6 ni ayirish.

$$\frac{2\sqrt{3}\left(7-\sqrt{6}\right)}{43}$$

2\sqrt{3} ga 7-\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{14\sqrt{3}-2\sqrt{3}\sqrt{6}}{43}$$

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

$$\frac{14\sqrt{3}-2\sqrt{3}\sqrt{3}\sqrt{2}}{43}$$

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

$$\frac{14\sqrt{3}-2\times 3\sqrt{2}}{43}$$

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

$$\frac{14\sqrt{3}-6\sqrt{2}}{43}$$