Rešite 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}=

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

Ovrednoti

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

Koraki rešitve

Izračunajte \sqrt[5]{\frac{1}{32}} in dobite \frac{1}{2}.

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

Izračunajte potenco \frac{2}{3} števila -1, da dobite \frac{3}{2}.

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

Delite \frac{1}{2} s/z \frac{3}{2} tako, da pomnožite \frac{1}{2} z obratno vrednostjo \frac{3}{2}.

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

Pomnožite \frac{1}{2} in \frac{2}{3}, da dobite \frac{1}{3}.

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

Odštejte \frac{1}{3} od 1, da dobite \frac{2}{3}.

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

Zmanjšajte ulomek \frac{2}{4} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

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

Pomnožite \frac{2}{3} in \frac{1}{2}, da dobite \frac{1}{3}.

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

Seštejte \frac{1}{3} in \frac{1}{2}, da dobite \frac{5}{6}.

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

Delite \frac{1}{3} s/z \frac{5}{6} tako, da pomnožite \frac{1}{3} z obratno vrednostjo \frac{5}{6}.

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

Pomnožite \frac{1}{3} in \frac{6}{5}, da dobite \frac{2}{5}.

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

Odštejte \frac{16}{25} od 1, da dobite \frac{9}{25}.

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

Znova napišite kvadratni koren deljenja \frac{9}{25} kot deljenje kvadratnih korenov \frac{\sqrt{9}}{\sqrt{25}}. Vzemite kvadratni koren števca in imenovalca.

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

Izračunajte potenco \frac{15}{2} števila 1, da dobite \frac{15}{2}.

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

Delite \frac{4}{5} s/z \frac{15}{2} tako, da pomnožite \frac{4}{5} z obratno vrednostjo \frac{15}{2}.

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

Pomnožite \frac{4}{5} in \frac{2}{15}, da dobite \frac{8}{75}.

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

Delite \frac{3}{5} s/z \frac{8}{75} tako, da pomnožite \frac{3}{5} z obratno vrednostjo \frac{8}{75}.

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

Pomnožite \frac{3}{5} in \frac{75}{8}, da dobite \frac{45}{8}.

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

Seštejte \frac{2}{5} in \frac{45}{8}, da dobite \frac{241}{40}.

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

Faktoriziraj

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