Riješi 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)]}}

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

Procijeni

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

Koraci za rješenje

Pomnožite \frac{3}{2} i \frac{3}{10} da biste dobili \frac{9}{20}.

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

Oduzmite \frac{1}{3} od 2 da biste dobili \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 \frac{5}{3} stepen od 2 i dobijte \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} i \frac{25}{9} da biste dobili \frac{5}{3}.

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

Oduzmite \frac{5}{3} od \frac{9}{5} da biste dobili \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} i \frac{3}{2} da biste dobili \frac{1}{5}.

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

Saberite \frac{9}{20} i \frac{1}{5} da biste dobili \frac{13}{20}.

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

Saberite \frac{3}{5} i 2 da biste dobili \frac{13}{5}.

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

Podijelite \frac{13}{20} sa \frac{13}{5} tako što ćete pomnožiti \frac{13}{20} recipročnom vrijednošću od \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} i \frac{5}{13} da biste dobili \frac{1}{4}.

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

Saberite \frac{1}{4} i 3 da biste dobili \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} i \frac{13}{4} da biste dobili \frac{1}{2}.

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

Saberite \frac{1}{6} i \frac{1}{2} da biste dobili \frac{2}{3}.

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

Pomnožite \frac{2}{3} i \frac{2}{3} da biste dobili \frac{4}{9}.

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

Podijelite \frac{1}{4} sa \frac{4}{9} tako što ćete pomnožiti \frac{1}{4} recipročnom vrijednošću od \frac{4}{9}.

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

Pomnožite \frac{1}{4} i \frac{9}{4} da biste dobili \frac{9}{16}.

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

Ponovo napišite kvadratni korijen dijeljenja \frac{9}{16} kao dijeljenje kvadratnih korijena \frac{\sqrt{9}}{\sqrt{16}}. Uzmite kvadratni korijen brojioca i imenioca.

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

Faktor

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