sqrt{{3/2*3/10+[9/5-frac{3/5*(2-frac{1}{3})^2]*frac{3}{2}}:(frac{3}{5}+2)}{frac{2}{3}*[frac{1}{6}+frac{2}{13}*(frac{1}{4}+3)]}} eching

$$\sqrt { \frac { \{ \frac { 3 } { 2 } \times \frac { 3 } { 10 } + [ \frac { 9 } { 5 } - \frac { 3 } { 5 } \times ( 2 - \frac { 1 } { 3 } ) ^ { 2 } ] \times \frac { 3 } { 2 } \} : ( \frac { 3 } { 5 } + 2 ) } { \frac { 2 } { 3 } \times [ \frac { 1 } { 6 } + \frac { 2 } { 13 } \times ( \frac { 1 } { 4 } + 3 ) ] } }$$

Baholash

$$\frac{3}{4}=0,75$$

Yechim qadamlari

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

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\left(2-\frac{1}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{5}{3} olish uchun 2 dan \frac{1}{3} ni ayirish.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \left(\frac{5}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

2 daraja ko‘rsatkichini \frac{5}{3} ga hisoblang va \frac{25}{9} ni qiymatni oling.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \frac{25}{9}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{5}{3} hosil qilish uchun \frac{3}{5} va \frac{25}{9} ni ko'paytirish.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{5}{3}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{2}{15} olish uchun \frac{9}{5} dan \frac{5}{3} ni ayirish.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{2}{15}\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{1}{5} hosil qilish uchun \frac{2}{15} va \frac{3}{2} ni ko'paytirish.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{1}{5}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{13}{20} olish uchun \frac{9}{20} va \frac{1}{5}'ni qo'shing.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{13}{5} olish uchun \frac{3}{5} va 2'ni qo'shing.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{13}{5}}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{13}{20} ni \frac{13}{5} ga bo'lish \frac{13}{20} ga k'paytirish \frac{13}{5} ga qaytarish.

$$\sqrt{\frac{\frac{13}{20}\times \frac{5}{13}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{1}{4} hosil qilish uchun \frac{13}{20} va \frac{5}{13} ni ko'paytirish.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

\frac{13}{4} olish uchun \frac{1}{4} va 3'ni qo'shing.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\times \frac{13}{4}\right)}}$$

\frac{1}{2} hosil qilish uchun \frac{2}{13} va \frac{13}{4} ni ko'paytirish.

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

\frac{2}{3} olish uchun \frac{1}{6} va \frac{1}{2}'ni qo'shing.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\times \frac{2}{3}}}$$

\frac{4}{9} hosil qilish uchun \frac{2}{3} va \frac{2}{3} ni ko'paytirish.

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

\frac{1}{4} ni \frac{4}{9} ga bo'lish \frac{1}{4} ga k'paytirish \frac{4}{9} ga qaytarish.

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

\frac{9}{16} hosil qilish uchun \frac{1}{4} va \frac{9}{4} ni ko'paytirish.

$$\sqrt{\frac{9}{16}}$$

\frac{9}{16} boʻlinmasining kvadrat ildizini \frac{\sqrt{9}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{3}{4}$$

Omil

$$\frac{3}{2 ^ {2}} = 0,75$$