Rešite sqrt{{(1+3/4-1/2)^2:[1-(5/4-1/2)]^2*(frac{2}{5}:frac{5}{4})*frac{1}{14}}*frac{4}{7}}

$$\sqrt { \{ ( 1 + \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } : [ 1 - ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ] ^ { 2 } \cdot ( \frac { 2 } { 5 } : \frac { 5 } { 4 } ) \cdot \frac { 1 } { 14 } \} \cdot \frac { 4 } { 7 } }$$

Ovrednoti

$$\frac{4}{7}\approx 0,571428571$$

Koraki rešitve

Seštejte 1 in \frac{3}{4}, da dobite \frac{7}{4}.

$$\sqrt{\frac{\left(\frac{7}{4}-\frac{1}{2}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Odštejte \frac{1}{2} od \frac{7}{4}, da dobite \frac{5}{4}.

$$\sqrt{\frac{\left(\frac{5}{4}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Izračunajte potenco \frac{5}{4} števila 2, da dobite \frac{25}{16}.

$$\sqrt{\frac{\frac{25}{16}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Odštejte \frac{1}{2} od \frac{5}{4}, da dobite \frac{3}{4}.

$$\sqrt{\frac{\frac{25}{16}}{\left(1-\frac{3}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Odštejte \frac{3}{4} od 1, da dobite \frac{1}{4}.

$$\sqrt{\frac{\frac{25}{16}}{\left(\frac{1}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Izračunajte potenco \frac{1}{4} števila 2, da dobite \frac{1}{16}.

$$\sqrt{\frac{\frac{25}{16}}{\frac{1}{16}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Delite \frac{25}{16} s/z \frac{1}{16} tako, da pomnožite \frac{25}{16} z obratno vrednostjo \frac{1}{16}.

$$\sqrt{\frac{25}{16}\times 16\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Pomnožite \frac{25}{16} in 16, da dobite 25.

$$\sqrt{25\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Delite \frac{2}{5} s/z \frac{5}{4} tako, da pomnožite \frac{2}{5} z obratno vrednostjo \frac{5}{4}.

$$\sqrt{25\times \frac{2}{5}\times \frac{4}{5}\times \frac{1}{14}\times \frac{4}{7}}$$

Pomnožite \frac{2}{5} in \frac{4}{5}, da dobite \frac{8}{25}.

$$\sqrt{25\times \frac{8}{25}\times \frac{1}{14}\times \frac{4}{7}}$$

Pomnožite 25 in \frac{8}{25}, da dobite 8.

$$\sqrt{8\times \frac{1}{14}\times \frac{4}{7}}$$

Pomnožite 8 in \frac{1}{14}, da dobite \frac{4}{7}.

$$\sqrt{\frac{4}{7}\times \frac{4}{7}}$$

Pomnožite \frac{4}{7} in \frac{4}{7}, da dobite \frac{16}{49}.

$$\sqrt{\frac{16}{49}}$$

Znova napišite kvadratni koren deljenja \frac{16}{49} kot deljenje kvadratnih korenov \frac{\sqrt{16}}{\sqrt{49}}. Vzemite kvadratni koren števca in imenovalca.

$$\frac{4}{7}$$

Faktoriziraj

$$\frac{2 ^ {2}}{7} = 0,5714285714285714$$