Issolvi [(sqrt{2})^{2}*(2/sqrt{3})^2][(1/2)^2+4*1^2-2^2]

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

Evalwa

$$\frac{2}{3}\approx 0.666666667$$

Passi tas-Soluzzjonijiet

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Irrazzjonalizza d-denominatur tal-\frac{2}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Biex tgħolli \frac{2\sqrt{3}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Ikkalkula \frac{1}{2} bil-power ta' 2 u tikseb \frac{1}{4}.

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

Ikkalkula 1 bil-power ta' 2 u tikseb 1.

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

Immultiplika 4 u 1 biex tikseb 4.

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

Żid \frac{1}{4} u 4 biex tikseb \frac{17}{4}.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-2^{2}\right)$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$2\times \frac{\left(2\sqrt{3}\right)^{2}}{3^{2}}\left(\frac{17}{4}-4\right)$$

Naqqas 4 minn \frac{17}{4} biex tikseb \frac{1}{4}.

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

Immultiplika 2 u \frac{1}{4} biex tikseb \frac{1}{2}.

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

Espandi \left(2\sqrt{3}\right)^{2}.

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

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

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

Il-kwadrat ta' \sqrt{3} huwa 3.

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

Immultiplika 4 u 3 biex tikseb 12.

$$\frac{1}{2}\times \frac{12}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{1}{2}\times \frac{12}{9}$$

Naqqas il-frazzjoni \frac{12}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

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

Immultiplika \frac{1}{2} u \frac{4}{3} biex tikseb \frac{2}{3}.

$$\frac{2}{3}$$

Fattur

$$\frac{2}{3} = 0.6666666666666666$$