Atrisiniet 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}}

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

Izrēķināt

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

Atrisinājuma darbības

Aprēķināt \sqrt[5]{\frac{1}{32}} un iegūt \frac{1}{2}.

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

Aprēķiniet \frac{2}{3} pakāpē -1 un iegūstiet \frac{3}{2}.

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

Daliet \frac{1}{2} ar \frac{3}{2}, reizinot \frac{1}{2} ar apgriezto daļskaitli \frac{3}{2} .

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

Reiziniet \frac{1}{2} un \frac{2}{3}, lai iegūtu \frac{1}{3}.

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

Atņemiet \frac{1}{3} no 1, lai iegūtu \frac{2}{3}.

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

Reiziniet \frac{2}{3} un \frac{9}{4}, lai iegūtu \frac{3}{2}.

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

Saskaitiet \frac{3}{2} un \frac{1}{2}, lai iegūtu 2.

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

Izsakiet \frac{\frac{1}{3}}{2} kā vienu daļskaitli.

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

Reiziniet 3 un 2, lai iegūtu 6.

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

Atņemiet \frac{16}{25} no 1, lai iegūtu \frac{9}{25}.

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

Pārrakstiet dalījuma kvadrātsakni \frac{9}{25} kā kvadrātveida saknes \frac{\sqrt{9}}{\sqrt{25}}. Izrēķiniet gan skaitītāja, gan saucēja kvadrātsakni.

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

Aprēķiniet \frac{15}{2} pakāpē 1 un iegūstiet \frac{15}{2}.

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

Daliet \frac{4}{5} ar \frac{15}{2}, reizinot \frac{4}{5} ar apgriezto daļskaitli \frac{15}{2} .

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

Reiziniet \frac{4}{5} un \frac{2}{15}, lai iegūtu \frac{8}{75}.

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

Daliet \frac{3}{5} ar \frac{8}{75}, reizinot \frac{3}{5} ar apgriezto daļskaitli \frac{8}{75} .

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

Reiziniet \frac{3}{5} un \frac{75}{8}, lai iegūtu \frac{45}{8}.

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

Saskaitiet \frac{1}{6} un \frac{45}{8}, lai iegūtu \frac{139}{24}.

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

Sadalīt reizinātājos

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