Riješi sqrt{4/3*(1/2)^2*(10/7-3/7)^2*frac{3}{2}+(frac{1}{2}-frac{1}{4})*6-[(frac{1}{4})^2:(frac{1}{4}:4)]^3}

$$\sqrt { \frac { 4 } { 3 } \times ( \frac { 1 } { 2 } ) ^ { 2 } \times ( \frac { 10 } { 7 } - \frac { 3 } { 7 } ) ^ { 2 } \times \frac { 3 } { 2 } + ( \frac { 1 } { 2 } - \frac { 1 } { 4 } ) \times 6 - [ ( \frac { 1 } { 4 } ) ^ { 2 } : ( \frac { 1 } { 4 } : 4 ) ] ^ { 3 } }$$

Procijeni

$$1$$

Koraci za rješenje

Izračunajte \frac{1}{2} stepen od 2 i dobijte \frac{1}{4}.

$$\sqrt{\frac{4}{3}\times \frac{1}{4}\left(\frac{10}{7}-\frac{3}{7}\right)^{2}\times \frac{3}{2}+\left(\frac{1}{2}-\frac{1}{4}\right)\times 6-\left(\frac{\left(\frac{1}{4}\right)^{2}}{\frac{\frac{1}{4}}{4}}\right)^{3}}$$

Pomnožite \frac{4}{3} i \frac{1}{4} da biste dobili \frac{1}{3}.

$$\sqrt{\frac{1}{3}\left(\frac{10}{7}-\frac{3}{7}\right)^{2}\times \frac{3}{2}+\left(\frac{1}{2}-\frac{1}{4}\right)\times 6-\left(\frac{\left(\frac{1}{4}\right)^{2}}{\frac{\frac{1}{4}}{4}}\right)^{3}}$$

Oduzmite \frac{3}{7} od \frac{10}{7} da biste dobili 1.

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

Izračunajte 1 stepen od 2 i dobijte 1.

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

Pomnožite \frac{1}{3} i 1 da biste dobili \frac{1}{3}.

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

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

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

Oduzmite \frac{1}{4} od \frac{1}{2} da biste dobili \frac{1}{4}.

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

Pomnožite \frac{1}{4} i 6 da biste dobili \frac{3}{2}.

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

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

$$\sqrt{2-\left(\frac{\left(\frac{1}{4}\right)^{2}}{\frac{\frac{1}{4}}{4}}\right)^{3}}$$

Izračunajte \frac{1}{4} stepen od 2 i dobijte \frac{1}{16}.

$$\sqrt{2-\left(\frac{\frac{1}{16}}{\frac{\frac{1}{4}}{4}}\right)^{3}}$$

Izrazite \frac{\frac{1}{4}}{4} kao jedan razlomak.

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

Pomnožite 4 i 4 da biste dobili 16.

$$\sqrt{2-\left(\frac{\frac{1}{16}}{\frac{1}{16}}\right)^{3}}$$

Podijelite \frac{1}{16} sa \frac{1}{16} da biste dobili 1.

$$\sqrt{2-1^{3}}$$

Izračunajte 1 stepen od 3 i dobijte 1.

$$\sqrt{2-1}$$

Oduzmite 1 od 2 da biste dobili 1.

$$\sqrt{1}$$

Izračunajte kvadratni koren od 1 i dobijte 1.

$$1$$

Faktor

$$1$$