Rešite sqrt{{3/2*3/10+[9/5-frac{3/5*(2-frac{1}{3})^2]*frac{3}{2}}:(frac{3}{5}+2)}{frac{2}{3}*[frac{1}{6}+frac{2}{13}*(frac{1}{4}+3)]}}

$$\sqrt { \frac { \{ \frac { 3 } { 2 } \times \frac { 3 } { 10 } + [ \frac { 9 } { 5 } - \frac { 3 } { 5 } \times ( 2 - \frac { 1 } { 3 } ) ^ { 2 } ] \times \frac { 3 } { 2 } \} : ( \frac { 3 } { 5 } + 2 ) } { \frac { 2 } { 3 } \times [ \frac { 1 } { 6 } + \frac { 2 } { 13 } \times ( \frac { 1 } { 4 } + 3 ) ] } }$$

Ovrednoti

$$\frac{3}{4}=0,75$$

Koraki rešitve

Pomnožite \frac{3}{2} in \frac{3}{10}, da dobite \frac{9}{20}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\left(2-\frac{1}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Odštejte \frac{1}{3} od 2, da dobite \frac{5}{3}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \left(\frac{5}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Izračunajte potenco \frac{5}{3} števila 2, da dobite \frac{25}{9}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \frac{25}{9}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Pomnožite \frac{3}{5} in \frac{25}{9}, da dobite \frac{5}{3}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{5}{3}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Odštejte \frac{5}{3} od \frac{9}{5}, da dobite \frac{2}{15}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{2}{15}\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Pomnožite \frac{2}{15} in \frac{3}{2}, da dobite \frac{1}{5}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{1}{5}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Seštejte \frac{9}{20} in \frac{1}{5}, da dobite \frac{13}{20}.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Seštejte \frac{3}{5} in 2, da dobite \frac{13}{5}.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{13}{5}}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Delite \frac{13}{20} s/z \frac{13}{5} tako, da pomnožite \frac{13}{20} z obratno vrednostjo \frac{13}{5}.

$$\sqrt{\frac{\frac{13}{20}\times \frac{5}{13}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Pomnožite \frac{13}{20} in \frac{5}{13}, da dobite \frac{1}{4}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Seštejte \frac{1}{4} in 3, da dobite \frac{13}{4}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\times \frac{13}{4}\right)}}$$

Pomnožite \frac{2}{13} in \frac{13}{4}, da dobite \frac{1}{2}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{1}{2}\right)}}$$

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

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\times \frac{2}{3}}}$$

Pomnožite \frac{2}{3} in \frac{2}{3}, da dobite \frac{4}{9}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{4}{9}}}$$

Delite \frac{1}{4} s/z \frac{4}{9} tako, da pomnožite \frac{1}{4} z obratno vrednostjo \frac{4}{9}.

$$\sqrt{\frac{1}{4}\times \frac{9}{4}}$$

Pomnožite \frac{1}{4} in \frac{9}{4}, da dobite \frac{9}{16}.

$$\sqrt{\frac{9}{16}}$$

Znova napišite kvadratni koren deljenja \frac{9}{16} kot deljenje kvadratnih korenov \frac{\sqrt{9}}{\sqrt{16}}. Vzemite kvadratni koren števca in imenovalca.

$$\frac{3}{4}$$

Faktoriziraj

$$\frac{3}{2 ^ {2}} = 0,75$$