Rešite sqrt{6*{5/13*[7/3*(1/3+2):(2+1/2):(frac{5}{6}+frac{3}{2})+(1-frac{1}{5})]-frac{1}{2}}*{frac{5}{9}*[(frac{2}{15}+frac{5}{3}):frac{5}{2}]}^2}

$$\sqrt { 6 \times \{ \frac { 5 } { 13 } \times [ \frac { 7 } { 3 } \times ( \frac { 1 } { 3 } + 2 ) : ( 2 + \frac { 1 } { 2 } ) : ( \frac { 5 } { 6 } + \frac { 3 } { 2 } ) + ( 1 - \frac { 1 } { 5 } ) ] - \frac { 1 } { 2 } \} \times \{ \frac { 5 } { 9 } \times [ ( \frac { 2 } { 15 } + \frac { 5 } { 3 } ) : \frac { 5 } { 2 } ] \} ^ { 2 } }$$

Ovrednoti

$$\frac{2}{5}=0,4$$

Koraki rešitve

Seštejte \frac{1}{3} in 2, da dobite \frac{7}{3}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{7}{3}\times \frac{7}{3}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Pomnožite \frac{7}{3} in \frac{7}{3}, da dobite \frac{49}{9}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

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

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{\frac{5}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Delite \frac{49}{9} s/z \frac{5}{2} tako, da pomnožite \frac{49}{9} z obratno vrednostjo \frac{5}{2}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{49}{9}\times \frac{2}{5}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Pomnožite \frac{49}{9} in \frac{2}{5}, da dobite \frac{98}{45}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Seštejte \frac{5}{6} in \frac{3}{2}, da dobite \frac{7}{3}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{7}{3}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Delite \frac{98}{45} s/z \frac{7}{3} tako, da pomnožite \frac{98}{45} z obratno vrednostjo \frac{7}{3}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{98}{45}\times \frac{3}{7}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Pomnožite \frac{98}{45} in \frac{3}{7}, da dobite \frac{14}{15}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{14}{15}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Seštejte \frac{14}{15} in 1, da dobite \frac{29}{15}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{29}{15}-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Odštejte \frac{1}{5} od \frac{29}{15}, da dobite \frac{26}{15}.

$$\sqrt{6\left(\frac{5}{13}\times \frac{26}{15}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Pomnožite \frac{5}{13} in \frac{26}{15}, da dobite \frac{2}{3}.

$$\sqrt{6\left(\frac{2}{3}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Odštejte \frac{1}{2} od \frac{2}{3}, da dobite \frac{1}{6}.

$$\sqrt{6\times \frac{1}{6}\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

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

$$\sqrt{\left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Seštejte \frac{2}{15} in \frac{5}{3}, da dobite \frac{9}{5}.

$$\sqrt{\left(\frac{5}{9}\times \frac{\frac{9}{5}}{\frac{5}{2}}\right)^{2}}$$

Delite \frac{9}{5} s/z \frac{5}{2} tako, da pomnožite \frac{9}{5} z obratno vrednostjo \frac{5}{2}.

$$\sqrt{\left(\frac{5}{9}\times \frac{9}{5}\times \frac{2}{5}\right)^{2}}$$

Pomnožite \frac{9}{5} in \frac{2}{5}, da dobite \frac{18}{25}.

$$\sqrt{\left(\frac{5}{9}\times \frac{18}{25}\right)^{2}}$$

Pomnožite \frac{5}{9} in \frac{18}{25}, da dobite \frac{2}{5}.

$$\sqrt{\left(\frac{2}{5}\right)^{2}}$$

Izračunajte potenco \frac{2}{5} števila 2, da dobite \frac{4}{25}.

$$\sqrt{\frac{4}{25}}$$

Znova napišite kvadratni koren deljenja \frac{4}{25} kot deljenje kvadratnih korenov \frac{\sqrt{4}}{\sqrt{25}}. Vzemite kvadratni koren števca in imenovalca.

$$\frac{2}{5}$$

Faktoriziraj

$$\frac{2}{5} = 0,4$$