Issolvi sqrt{{[(2/3+1/2)-1/6]^2}^3+1-(2/3+frac{7}{6}+frac{2}{12})+[15*(frac{1}{3}+frac{1}{5})]^2}

$$\sqrt { \{ [ ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) - \frac { 1 } { 6 } ] ^ { 2 } \} ^ { 3 } + 1 - ( \frac { 2 } { 3 } + \frac { 7 } { 6 } + \frac { 2 } { 12 } ) + [ 15 \times ( \frac { 1 } { 3 } + \frac { 1 } { 5 } ) ] ^ { 2 } }$$

Evalwa

$$8$$

Passi tas-Soluzzjonijiet

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 2 u 3 biex tikseb 6.

$$\sqrt{\left(\frac{2}{3}+\frac{1}{2}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Żid \frac{2}{3} u \frac{1}{2} biex tikseb \frac{7}{6}.

$$\sqrt{\left(\frac{7}{6}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Naqqas \frac{1}{6} minn \frac{7}{6} biex tikseb 1.

$$\sqrt{1^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Ikkalkula 1 bil-power ta' 6 u tikseb 1.

$$\sqrt{1+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Żid 1 u 1 biex tikseb 2.

$$\sqrt{2-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Żid \frac{2}{3} u \frac{7}{6} biex tikseb \frac{11}{6}.

$$\sqrt{2-\left(\frac{11}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Naqqas il-frazzjoni \frac{2}{12} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\sqrt{2-\left(\frac{11}{6}+\frac{1}{6}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Żid \frac{11}{6} u \frac{1}{6} biex tikseb 2.

$$\sqrt{2-2+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Naqqas 2 minn 2 biex tikseb 0.

$$\sqrt{0+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Żid \frac{1}{3} u \frac{1}{5} biex tikseb \frac{8}{15}.

$$\sqrt{0+\left(15\times \frac{8}{15}\right)^{2}}$$

Immultiplika 15 u \frac{8}{15} biex tikseb 8.

$$\sqrt{0+8^{2}}$$

Ikkalkula 8 bil-power ta' 2 u tikseb 64.

$$\sqrt{0+64}$$

Żid 0 u 64 biex tikseb 64.

$$\sqrt{64}$$

Ikkalkula l-għerq kwadrat ta' 64 u ikseb 8.

$$8$$

Fattur

$$2^{3}$$