sqrt[5]{frac{1/32}:(2/3)^-1}{(1-1/3)2/4+frac{1}{2}}+frac{sqrt{1-frac{16}{25}}}{frac{4}{5}:(frac{15}{2})^1}= eching

$$\frac { \sqrt[ 5 ] { \frac { 1 } { 32 } } : ( \frac { 2 } { 3 } ) ^ { - 1 } } { ( 1 - \frac { 1 } { 3 } ) \frac { 2 } { 4 } + \frac { 1 } { 2 } } + \frac { \sqrt { 1 - \frac { 16 } { 25 } } } { \frac { 4 } { 5 } : ( \frac { 15 } { 2 } ) ^ { 1 } } =$$

Baholash

$$\frac{241}{40}=6,025$$

Yechim qadamlari

\sqrt[5]{\frac{1}{32}} ni hisoblab, \frac{1}{2} natijasiga ega bo‘ling.

$$\frac{\frac{\frac{1}{2}}{\left(\frac{2}{3}\right)^{-1}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

-1 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{3}{2} ni qiymatni oling.

$$\frac{\frac{\frac{1}{2}}{\frac{3}{2}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{2}\times \frac{2}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{1}{2}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{5}{6} olish uchun \frac{1}{3} va \frac{1}{2}'ni qo'shing.

$$\frac{\frac{1}{3}}{\frac{5}{6}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{1}{3} ni \frac{5}{6} ga bo'lish \frac{1}{3} ga k'paytirish \frac{5}{6} ga qaytarish.

$$\frac{1}{3}\times \frac{6}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{2}{5} hosil qilish uchun \frac{1}{3} va \frac{6}{5} ni ko'paytirish.

$$\frac{2}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{9}{25} olish uchun 1 dan \frac{16}{25} ni ayirish.

$$\frac{2}{5}+\frac{\sqrt{\frac{9}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

\frac{9}{25} boʻlinmasining kvadrat ildizini \frac{\sqrt{9}}{\sqrt{25}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

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

1 daraja ko‘rsatkichini \frac{15}{2} ga hisoblang va \frac{15}{2} ni qiymatni oling.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\frac{15}{2}}}$$

\frac{4}{5} ni \frac{15}{2} ga bo'lish \frac{4}{5} ga k'paytirish \frac{15}{2} ga qaytarish.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{4}{5}\times \frac{2}{15}}$$

\frac{8}{75} hosil qilish uchun \frac{4}{5} va \frac{2}{15} ni ko'paytirish.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{8}{75}}$$

\frac{3}{5} ni \frac{8}{75} ga bo'lish \frac{3}{5} ga k'paytirish \frac{8}{75} ga qaytarish.

$$\frac{2}{5}+\frac{3}{5}\times \frac{75}{8}$$

\frac{45}{8} hosil qilish uchun \frac{3}{5} va \frac{75}{8} ni ko'paytirish.

$$\frac{2}{5}+\frac{45}{8}$$

\frac{241}{40} olish uchun \frac{2}{5} va \frac{45}{8}'ni qo'shing.

$$\frac{241}{40}$$

Omil

$$\frac{241}{2 ^ {3} \cdot 5} = 6\frac{1}{40} = 6,025$$