frac{sqrt{3}-sqrt{2}}{sqrt{2}+sqrt{3}} eching

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

Baholash

$$5-2\sqrt{6}\approx 0,101020514$$

Yechim qadamlari

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

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

Hisoblang: \left(\sqrt{2}+\sqrt{3}\right)\left(\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}.

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

\sqrt{2} kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

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

-1 olish uchun 2 dan 3 ni ayirish.

$$\frac{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{2}-\sqrt{3}\right)}{-1}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

\sqrt{2} kvadrati – 2.

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

-5 olish uchun -3 dan 2 ni ayirish.

$$-\left(\sqrt{6}-5+\sqrt{3}\sqrt{2}\right)$$

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

$$-\left(\sqrt{6}-5+\sqrt{6}\right)$$

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

$$-\left(2\sqrt{6}-5\right)$$

2\sqrt{6}-5 teskarisini topish uchun har birining teskarisini toping.

$$-2\sqrt{6}-\left(-5\right)$$

-5 ning teskarisi 5 ga teng.

$$-2\sqrt{6}+5$$