Rešite sqrt{{8/3-1/2-[(1+1/3)^2:4/3+frac{1}{5}]*frac{5}{46}+(2-frac{1}{4})}:frac{3}{5}}

$$\sqrt { \{ \frac { 8 } { 3 } - \frac { 1 } { 2 } - [ ( 1 + \frac { 1 } { 3 } ) ^ { 2 } : \frac { 4 } { 3 } + \frac { 1 } { 5 } ] \times \frac { 5 } { 46 } + ( 2 - \frac { 1 } { 4 } ) \} : \frac { 3 } { 5 } }$$

Ovrednoti

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

Koraki rešitve

Odštejte \frac{1}{2} od \frac{8}{3}, da dobite \frac{13}{6}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(1+\frac{1}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

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

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(\frac{4}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Izračunajte potenco \frac{4}{3} števila 2, da dobite \frac{16}{9}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\frac{16}{9}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Delite \frac{16}{9} s/z \frac{4}{3} tako, da pomnožite \frac{16}{9} z obratno vrednostjo \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{16}{9}\times \frac{3}{4}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Pomnožite \frac{16}{9} in \frac{3}{4}, da dobite \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{4}{3}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Seštejte \frac{4}{3} in \frac{1}{5}, da dobite \frac{23}{15}.

$$\sqrt{\frac{\frac{13}{6}-\frac{23}{15}\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Pomnožite \frac{23}{15} in \frac{5}{46}, da dobite \frac{1}{6}.

$$\sqrt{\frac{\frac{13}{6}-\frac{1}{6}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Odštejte \frac{1}{6} od \frac{13}{6}, da dobite 2.

$$\sqrt{\frac{2+2-\frac{1}{4}}{\frac{3}{5}}}$$

Seštejte 2 in 2, da dobite 4.

$$\sqrt{\frac{4-\frac{1}{4}}{\frac{3}{5}}}$$

Odštejte \frac{1}{4} od 4, da dobite \frac{15}{4}.

$$\sqrt{\frac{\frac{15}{4}}{\frac{3}{5}}}$$

Delite \frac{15}{4} s/z \frac{3}{5} tako, da pomnožite \frac{15}{4} z obratno vrednostjo \frac{3}{5}.

$$\sqrt{\frac{15}{4}\times \frac{5}{3}}$$

Pomnožite \frac{15}{4} in \frac{5}{3}, da dobite \frac{25}{4}.

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

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

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

Faktoriziraj

$$\frac{5}{2} = 2\frac{1}{2} = 2,5$$