frac{sqrt[5]{frac{1/32}}{{left(2/3right)}^-1}}{left(1-1/3right)9/4+frac{1}{2}}+frac{sqrt{1-frac{16}{25}}}{frac{frac{4}{5}}{{left(frac{15}{2}right)}^1}} eching

$$\frac{ \frac{ \sqrt[ 5 ]{ \frac{ 1 }{ 32 } } }{ { \left( \frac{ 2 }{ 3 } \right) }^{ -1 } } }{ \left( 1- \frac{ 1 }{ 3 } \right) \frac{ 9 }{ 4 } + \frac{ 1 }{ 2 } } + \frac{ \sqrt{ 1- \frac{ 16 }{ 25 } } }{ \frac{ \frac{ 4 }{ 5 } }{ { \left( \frac{ 15 }{ 2 } \right) }^{ 1 } } }$$

Baholash

$$\frac{139}{24}\approx 5,791666667$$

Yechim qadamlari

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

$$\frac{\frac{\frac{1}{2}}{\left(\frac{2}{3}\right)^{-1}}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{\frac{1}{2}}{\frac{3}{2}}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{2}\times \frac{2}{3}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

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

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

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

\frac{\frac{1}{3}}{2} ni yagona kasrga aylantiring.

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

6 hosil qilish uchun 3 va 2 ni ko'paytirish.

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

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

$$\frac{1}{6}+\frac{\sqrt{\frac{9}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

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

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\frac{15}{2}}}$$

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{4}{5}\times \frac{2}{15}}$$

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{8}{75}}$$

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

$$\frac{1}{6}+\frac{3}{5}\times \frac{75}{8}$$

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

$$\frac{1}{6}+\frac{45}{8}$$

\frac{139}{24} olish uchun \frac{1}{6} va \frac{45}{8}'ni qo'shing.

$$\frac{139}{24}$$

Omil

$$\frac{139}{2 ^ {3} \cdot 3} = 5\frac{19}{24} = 5,791666666666667$$