sqrt{{3/2+1-3/2*[(1/6*3/5+frac{7}{5}*frac{1}{7})*frac{5}{2}]}*frac{4}{33}+(1-frac{1}{2})^2:3+(frac{2}{3})^2} eching

$$\sqrt { \{ \frac { 3 } { 2 } + 1 - \frac { 3 } { 2 } \times [ ( \frac { 1 } { 6 } \times \frac { 3 } { 5 } + \frac { 7 } { 5 } \times \frac { 1 } { 7 } ) \times \frac { 5 } { 2 } ] \} \times \frac { 4 } { 33 } + ( 1 - \frac { 1 } { 2 } ) ^ { 2 } : 3 + ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Baholash

$$\frac{5}{6}\approx 0,833333333$$

Yechim qadamlari

\frac{5}{2} olish uchun \frac{3}{2} va 1'ni qo'shing.

$$\sqrt{\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{6}\times \frac{3}{5}+\frac{7}{5}\times \frac{1}{7}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{1}{10} hosil qilish uchun \frac{1}{6} va \frac{3}{5} ni ko'paytirish.

$$\sqrt{\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{10}+\frac{7}{5}\times \frac{1}{7}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{1}{5} hosil qilish uchun \frac{7}{5} va \frac{1}{7} ni ko'paytirish.

$$\sqrt{\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{10}+\frac{1}{5}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{3}{10} olish uchun \frac{1}{10} va \frac{1}{5}'ni qo'shing.

$$\sqrt{\left(\frac{5}{2}-\frac{3}{2}\times \frac{3}{10}\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{9}{20} hosil qilish uchun \frac{3}{2} va \frac{3}{10} ni ko'paytirish.

$$\sqrt{\left(\frac{5}{2}-\frac{9}{20}\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{9}{8} hosil qilish uchun \frac{9}{20} va \frac{5}{2} ni ko'paytirish.

$$\sqrt{\left(\frac{5}{2}-\frac{9}{8}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{11}{8} olish uchun \frac{5}{2} dan \frac{9}{8} ni ayirish.

$$\sqrt{\frac{11}{8}\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}}$$

\frac{1}{6} hosil qilish uchun \frac{11}{8} va \frac{4}{33} ni ko'paytirish.

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

\frac{1}{2} olish uchun 1 dan \frac{1}{2} ni ayirish.

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

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

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

\frac{\frac{1}{4}}{3} ni yagona kasrga aylantiring.

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

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

$$\sqrt{\frac{1}{6}+\frac{1}{12}+\left(\frac{2}{3}\right)^{2}}$$

\frac{1}{4} olish uchun \frac{1}{6} va \frac{1}{12}'ni qo'shing.

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

2 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{4}{9} ni qiymatni oling.

$$\sqrt{\frac{1}{4}+\frac{4}{9}}$$

\frac{25}{36} olish uchun \frac{1}{4} va \frac{4}{9}'ni qo'shing.

$$\sqrt{\frac{25}{36}}$$

\frac{25}{36} boʻlinmasining kvadrat ildizini \frac{\sqrt{25}}{\sqrt{36}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{5}{6}$$

Omil

$$\frac{5}{2 \cdot 3} = 0,8333333333333334$$