Rešite sqrt{3/4*{7/15+[3/5-(3/10*frac{2}{3})^2-(frac{2}{5})^3]:frac{8}{15}-(frac{9}{10})^2}}

$$\sqrt { \frac { 3 } { 4 } \times \{ \frac { 7 } { 15 } + [ \frac { 3 } { 5 } - ( \frac { 3 } { 10 } \times \frac { 2 } { 3 } ) ^ { 2 } - ( \frac { 2 } { 5 } ) ^ { 3 } ] : \frac { 8 } { 15 } - ( \frac { 9 } { 10 } ) ^ { 2 } \} }$$

Ovrednoti

$$\frac{\sqrt{11}}{5}\approx 0,663324958$$

Koraki rešitve

Pomnožite \frac{3}{10} in \frac{2}{3}, da dobite \frac{1}{5}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{\frac{3}{5}-\left(\frac{1}{5}\right)^{2}-\left(\frac{2}{5}\right)^{3}}{\frac{8}{15}}-\left(\frac{9}{10}\right)^{2}\right)}$$

Izračunajte potenco \frac{1}{5} števila 2, da dobite \frac{1}{25}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{\frac{3}{5}-\frac{1}{25}-\left(\frac{2}{5}\right)^{3}}{\frac{8}{15}}-\left(\frac{9}{10}\right)^{2}\right)}$$

Odštejte \frac{1}{25} od \frac{3}{5}, da dobite \frac{14}{25}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{\frac{14}{25}-\left(\frac{2}{5}\right)^{3}}{\frac{8}{15}}-\left(\frac{9}{10}\right)^{2}\right)}$$

Izračunajte potenco \frac{2}{5} števila 3, da dobite \frac{8}{125}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{\frac{14}{25}-\frac{8}{125}}{\frac{8}{15}}-\left(\frac{9}{10}\right)^{2}\right)}$$

Odštejte \frac{8}{125} od \frac{14}{25}, da dobite \frac{62}{125}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{\frac{62}{125}}{\frac{8}{15}}-\left(\frac{9}{10}\right)^{2}\right)}$$

Delite \frac{62}{125} s/z \frac{8}{15} tako, da pomnožite \frac{62}{125} z obratno vrednostjo \frac{8}{15}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{62}{125}\times \frac{15}{8}-\left(\frac{9}{10}\right)^{2}\right)}$$

Pomnožite \frac{62}{125} in \frac{15}{8}, da dobite \frac{93}{100}.

$$\sqrt{\frac{3}{4}\left(\frac{7}{15}+\frac{93}{100}-\left(\frac{9}{10}\right)^{2}\right)}$$

Seštejte \frac{7}{15} in \frac{93}{100}, da dobite \frac{419}{300}.

$$\sqrt{\frac{3}{4}\left(\frac{419}{300}-\left(\frac{9}{10}\right)^{2}\right)}$$

Izračunajte potenco \frac{9}{10} števila 2, da dobite \frac{81}{100}.

$$\sqrt{\frac{3}{4}\left(\frac{419}{300}-\frac{81}{100}\right)}$$

Odštejte \frac{81}{100} od \frac{419}{300}, da dobite \frac{44}{75}.

$$\sqrt{\frac{3}{4}\times \frac{44}{75}}$$

Pomnožite \frac{3}{4} in \frac{44}{75}, da dobite \frac{11}{25}.

$$\sqrt{\frac{11}{25}}$$

Znova napišite kvadratni koren deljenja \sqrt{\frac{11}{25}} kot deljenje kvadratnih korenov \frac{\sqrt{11}}{\sqrt{25}}.

$$\frac{\sqrt{11}}{\sqrt{25}}$$

Izračunajte kvadratni koren števila 25 in dobite 5.

$$\frac{\sqrt{11}}{5}$$