sqrt{{[(10/3-11/6)*4/15+3/5*(frac{2}{3}-frac{1}{2})]:frac{8}{3}+1-(frac{1}{2})^2}*(3+frac{3}{4})} eching

$$\sqrt { \{ [ ( \frac { 10 } { 3 } - \frac { 11 } { 6 } ) \times \frac { 4 } { 15 } + \frac { 3 } { 5 } \times ( \frac { 2 } { 3 } - \frac { 1 } { 2 } ) ] : \frac { 8 } { 3 } + 1 - ( \frac { 1 } { 2 } ) ^ { 2 } \} \times ( 3 + \frac { 3 } { 4 } ) }$$

Baholash

$$\frac{15}{8}=1,875$$

Yechim qadamlari

3 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{10}{3} va \frac{11}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{\left(\frac{20}{6}-\frac{11}{6}\right)\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{20}{6} va \frac{11}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\left(\frac{\frac{20-11}{6}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

9 olish uchun 20 dan 11 ni ayirish.

$$\sqrt{\left(\frac{\frac{9}{6}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{9}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{\frac{3}{2}\times \frac{4}{15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2} ni \frac{4}{15} ga ko‘paytiring.

$$\sqrt{\left(\frac{\frac{3\times 4}{2\times 15}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{3\times 4}{2\times 15} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\left(\frac{\frac{12}{30}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{12}{30} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\left(\frac{2}{3}-\frac{1}{2}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

3 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{2}{3} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\left(\frac{4}{6}-\frac{3}{6}\right)}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{4}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\times \frac{4-3}{6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

1 olish uchun 4 dan 3 ni ayirish.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{5}\times \frac{1}{6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{5} ni \frac{1}{6} ga ko‘paytiring.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3\times 1}{5\times 6}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{3\times 1}{5\times 6} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{3}{30}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{3}{30} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{\frac{2}{5}+\frac{1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

5 va 10 ning eng kichik umumiy karralisi 10 ga teng. \frac{2}{5} va \frac{1}{10} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{\frac{4}{10}+\frac{1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{4}{10} va \frac{1}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\left(\frac{\frac{4+1}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

5 olish uchun 4 va 1'ni qo'shing.

$$\sqrt{\left(\frac{\frac{5}{10}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{5}{10} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{\frac{1}{2}}{\frac{8}{3}}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{1}{2} ni \frac{8}{3} ga bo'lish \frac{1}{2} ga k'paytirish \frac{8}{3} ga qaytarish.

$$\sqrt{\left(\frac{1}{2}\times \frac{3}{8}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{3}{8} ga ko‘paytiring.

$$\sqrt{\left(\frac{1\times 3}{2\times 8}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{1\times 3}{2\times 8} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\left(\frac{3}{16}+1-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

1 ni \frac{16}{16} kasrga o‘giring.

$$\sqrt{\left(\frac{3}{16}+\frac{16}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

\frac{3}{16} va \frac{16}{16} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\left(\frac{3+16}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

19 olish uchun 3 va 16'ni qo'shing.

$$\sqrt{\left(\frac{19}{16}-\left(\frac{1}{2}\right)^{2}\right)\left(3+\frac{3}{4}\right)}$$

2 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\sqrt{\left(\frac{19}{16}-\frac{1}{4}\right)\left(3+\frac{3}{4}\right)}$$

16 va 4 ning eng kichik umumiy karralisi 16 ga teng. \frac{19}{16} va \frac{1}{4} ni 16 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\frac{19}{16}-\frac{4}{16}\right)\left(3+\frac{3}{4}\right)}$$

\frac{19}{16} va \frac{4}{16} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{19-4}{16}\left(3+\frac{3}{4}\right)}$$

15 olish uchun 19 dan 4 ni ayirish.

$$\sqrt{\frac{15}{16}\left(3+\frac{3}{4}\right)}$$

3 ni \frac{12}{4} kasrga o‘giring.

$$\sqrt{\frac{15}{16}\left(\frac{12}{4}+\frac{3}{4}\right)}$$

\frac{12}{4} va \frac{3}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{15}{16}\times \frac{12+3}{4}}$$

15 olish uchun 12 va 3'ni qo'shing.

$$\sqrt{\frac{15}{16}\times \frac{15}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{15}{16} ni \frac{15}{4} ga ko‘paytiring.

$$\sqrt{\frac{15\times 15}{16\times 4}}$$

\frac{15\times 15}{16\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{225}{64}}$$

\frac{225}{64} boʻlinmasining kvadrat ildizini \frac{\sqrt{225}}{\sqrt{64}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{15}{8}$$

Omil

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1,875$$