frac{sqrt{4}}{3}-2/3*[(2/7)]^2*2/7*(5^2/6*frac{2^2}{5}-1)-frac{1}{6}]+3= eching

$$\frac { \sqrt { 4 } } { 3 } - \frac { 2 } { 3 } \times [ ( \frac { 2 } { 7 } ) ] ^ { 2 } \cdot \frac { 2 } { 7 } \times ( \frac { 5 ^ { 2 } } { 6 } \times \frac { 2 ^ { 2 } } { 5 } - 1 ) - \frac { 1 } { 6 } ] + 3 =$$

Baholash

$$\frac{409}{882}\approx 0,463718821$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{\sqrt{4}}{3}-\frac{2}{3}\times \left(\frac{2}{7}\right)^{3}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$\frac{2}{3}-\frac{2}{3}\times \left(\frac{2}{7}\right)^{3}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

3 daraja ko‘rsatkichini \frac{2}{7} ga hisoblang va \frac{8}{343} ni qiymatni oling.

$$\frac{2}{3}-\frac{2}{3}\times \frac{8}{343}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2}{3} ni \frac{8}{343} ga ko‘paytiring.

$$\frac{2}{3}-\frac{2\times 8}{3\times 343}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

\frac{2\times 8}{3\times 343} kasridagi ko‘paytirishlarni bajaring.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

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

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

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

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25}{6}\times \frac{4}{5}-1\right)-\frac{1}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{25}{6} ni \frac{4}{5} ga ko‘paytiring.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25\times 4}{6\times 5}-1\right)-\frac{1}{6}$$

\frac{25\times 4}{6\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{100}{30}-1\right)-\frac{1}{6}$$

\frac{100}{30} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{10}{3}-1\right)-\frac{1}{6}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{10}{3}-\frac{3}{3}\right)-\frac{1}{6}$$

\frac{10}{3} va \frac{3}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{3}-\frac{16}{1029}\times \frac{10-3}{3}-\frac{1}{6}$$

7 olish uchun 10 dan 3 ni ayirish.

$$\frac{2}{3}-\frac{16}{1029}\times \frac{7}{3}-\frac{1}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{16}{1029} ni \frac{7}{3} ga ko‘paytiring.

$$\frac{2}{3}-\frac{16\times 7}{1029\times 3}-\frac{1}{6}$$

\frac{16\times 7}{1029\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{2}{3}-\frac{112}{3087}-\frac{1}{6}$$

\frac{112}{3087} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}-\frac{16}{441}-\frac{1}{6}$$

3 va 441 ning eng kichik umumiy karralisi 441 ga teng. \frac{2}{3} va \frac{16}{441} ni 441 maxraj bilan kasrlarga aylantirib oling.

$$\frac{294}{441}-\frac{16}{441}-\frac{1}{6}$$

\frac{294}{441} va \frac{16}{441} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{294-16}{441}-\frac{1}{6}$$

278 olish uchun 294 dan 16 ni ayirish.

$$\frac{278}{441}-\frac{1}{6}$$

441 va 6 ning eng kichik umumiy karralisi 882 ga teng. \frac{278}{441} va \frac{1}{6} ni 882 maxraj bilan kasrlarga aylantirib oling.

$$\frac{556}{882}-\frac{147}{882}$$

\frac{556}{882} va \frac{147}{882} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{556-147}{882}$$

409 olish uchun 556 dan 147 ni ayirish.

$$\frac{409}{882}$$

Omil

$$\frac{409}{2 \cdot 3 ^ {2} \cdot 7 ^ {2}} = 0,463718820861678$$