Issolvi (25/4)^2*(5/3)^2*(frac{sqrt{5}}{5})^2=

$$( \frac { 25 } { 4 } ) ^ { 2 } \times ( \frac { 5 } { 3 } ) ^ { 2 } \times ( \frac { \sqrt { 5 } } { 5 } ) ^ { 2 } =$$

Evalwa

$$\frac{3125}{144}\approx 21.701388889$$

Passi tas-Soluzzjonijiet

Ikkalkula \frac{25}{4} bil-power ta' 2 u tikseb \frac{625}{16}.

$$\frac{625}{16}\times \left(\frac{5}{3}\right)^{2}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

Ikkalkula \frac{5}{3} bil-power ta' 2 u tikseb \frac{25}{9}.

$$\frac{625}{16}\times \frac{25}{9}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

Immultiplika \frac{625}{16} u \frac{25}{9} biex tikseb \frac{15625}{144}.

$$\frac{15625}{144}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

Biex tgħolli \frac{\sqrt{5}}{5} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{15625}{144}\times \frac{\left(\sqrt{5}\right)^{2}}{5^{2}}$$

Immultiplika \frac{15625}{144} b'\frac{\left(\sqrt{5}\right)^{2}}{5^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{15625\left(\sqrt{5}\right)^{2}}{144\times 5^{2}}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{15625\times 5}{144\times 5^{2}}$$

Immultiplika 15625 u 5 biex tikseb 78125.

$$\frac{78125}{144\times 5^{2}}$$

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$\frac{78125}{144\times 25}$$

Immultiplika 144 u 25 biex tikseb 3600.

$$\frac{78125}{3600}$$

Naqqas il-frazzjoni \frac{78125}{3600} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 25.

$$\frac{3125}{144}$$

Fattur

$$\frac{5 ^ {5}}{2 ^ {4} \cdot 3 ^ {2}} = 21\frac{101}{144} = 21.70138888888889$$