=(3/sqrt{3})^2-2(3/sqrt{3})(5/sqrt{2})+(5/sqrt{2})^2 eching

$$= ( \frac { 3 } { \sqrt { 3 } } ) ^ { 2 } - 2 ( \frac { 3 } { \sqrt { 3 } } ) ( \frac { 5 } { \sqrt { 2 } } ) + ( \frac { 5 } { \sqrt { 2 } } ) ^ { 2 }$$

Baholash

$$\frac{31}{2}-5\sqrt{6}\approx 3,252551286$$

Yechim qadamlari

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

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

\sqrt{3} kvadrati – 3.

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

3 va 3 ni qisqartiring.

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

\sqrt{3} kvadrati – 3.

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

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

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

\sqrt{3} kvadrati – 3.

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

3 va 3 ni qisqartiring.

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

\frac{5}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

2 va 2 ni qisqartiring.

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

\frac{5}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

\frac{5\sqrt{2}}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

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

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

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

$$3-5\sqrt{6}+\frac{25\left(\sqrt{2}\right)^{2}}{2^{2}}$$

\sqrt{2} kvadrati – 2.

$$3-5\sqrt{6}+\frac{25\times 2}{2^{2}}$$

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

$$3-5\sqrt{6}+\frac{50}{2^{2}}$$

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

$$3-5\sqrt{6}+\frac{50}{4}$$

\frac{50}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$3-5\sqrt{6}+\frac{25}{2}$$

\frac{31}{2} olish uchun 3 va \frac{25}{2}'ni qo'shing.

$$\frac{31}{2}-5\sqrt{6}$$