1/sqrt{2}frac{sqrt{2}}{3}1/2sqrt{2} eching

$$\frac { 1 } { \sqrt { 2 } } \frac { \sqrt { 2 } } { 3 } \frac { 1 } { 2 \sqrt { 2 } }$$

Baholash

$$\frac{\sqrt{2}}{12}\approx 0,11785113$$

Yechim qadamlari

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

\frac{1}{2\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{2}}{2} ni \frac{\sqrt{2}}{3} ga ko‘paytiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{2}\sqrt{2}}{2\times 3} ni \frac{\sqrt{2}}{4} ga ko‘paytiring.

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

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

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

Surat va maxrajdagi ikkala 2 ni qisqartiring.

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

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$\frac{\sqrt{2}}{12}$$