(1/sqrt{2}*8sqrt{2}*2/3)*1/2 eching

$$( \frac { 1 } { \sqrt { 2 } } \times 8 \sqrt { 2 } \times \frac { 2 } { 3 } ) \times \frac { 1 } { 2 }$$

Baholash

$$\frac{8}{3}\approx 2,666666667$$

Yechim qadamlari

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

$$8\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

\sqrt{2} kvadrati – 2.

$$8\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

8\times \frac{2}{3} ni yagona kasrga aylantiring.

$$\frac{8\times 2}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

16 hosil qilish uchun 8 va 2 ni ko'paytirish.

$$\frac{16}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{16}{3} ni \frac{1}{2} ga ko‘paytiring.

$$\frac{16\times 1}{3\times 2}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

\frac{16\times 1}{3\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{16}{6}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

\frac{16}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{3} ni \frac{\sqrt{2}}{2} ga ko‘paytiring.

$$\frac{8\sqrt{2}}{3\times 2}\sqrt{2}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

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

\frac{4\sqrt{2}}{3}\sqrt{2} ni yagona kasrga aylantiring.

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

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

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

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

$$\frac{8}{3}$$

Omil

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2,6666666666666665$$