Issolvi (frac{4sqrt{13}}{13})^2+(frac{2sqrt{13}}{13}+1sqrt{13})^2

$$( \frac { 4 \sqrt { 13 } } { 13 } ) ^ { 2 } + ( \frac { 2 \sqrt { 13 } } { 13 } + 1 \sqrt { 13 } ) ^ { 2 }$$

Evalwa

$$\frac{241}{13}\approx 18.538461538$$

Passi tas-Soluzzjonijiet

Biex tgħolli \frac{4\sqrt{13}}{13} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\left(\frac{2\sqrt{13}}{13}+1\sqrt{13}\right)^{2}$$

Ikkombina \frac{2\sqrt{13}}{13} u 1\sqrt{13} biex tikseb \frac{15}{13}\sqrt{13}.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\left(\frac{15}{13}\sqrt{13}\right)^{2}$$

Espandi \left(\frac{15}{13}\sqrt{13}\right)^{2}.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\left(\frac{15}{13}\right)^{2}\left(\sqrt{13}\right)^{2}$$

Ikkalkula \frac{15}{13} bil-power ta' 2 u tikseb \frac{225}{169}.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\frac{225}{169}\left(\sqrt{13}\right)^{2}$$

Il-kwadrat ta' \sqrt{13} huwa 13.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\frac{225}{169}\times 13$$

Immultiplika \frac{225}{169} u 13 biex tikseb \frac{225}{13}.

$$\frac{\left(4\sqrt{13}\right)^{2}}{13^{2}}+\frac{225}{13}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 13^{2} u 13 huwa 169. Immultiplika \frac{225}{13} b'\frac{13}{13}.

$$\frac{\left(4\sqrt{13}\right)^{2}}{169}+\frac{225\times 13}{169}$$

Billi \frac{\left(4\sqrt{13}\right)^{2}}{169} u \frac{225\times 13}{169} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(4\sqrt{13}\right)^{2}+225\times 13}{169}$$

Espandi \left(4\sqrt{13}\right)^{2}.

$$\frac{4^{2}\left(\sqrt{13}\right)^{2}}{13^{2}}+\frac{225}{13}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$\frac{16\left(\sqrt{13}\right)^{2}}{13^{2}}+\frac{225}{13}$$

Il-kwadrat ta' \sqrt{13} huwa 13.

$$\frac{16\times 13}{13^{2}}+\frac{225}{13}$$

Immultiplika 16 u 13 biex tikseb 208.

$$\frac{208}{13^{2}}+\frac{225}{13}$$

Ikkalkula 13 bil-power ta' 2 u tikseb 169.

$$\frac{208}{169}+\frac{225}{13}$$

Naqqas il-frazzjoni \frac{208}{169} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 13.

$$\frac{16}{13}+\frac{225}{13}$$

Żid \frac{16}{13} u \frac{225}{13} biex tikseb \frac{241}{13}.

$$\frac{241}{13}$$

Fattur

$$\frac{241}{13} = 18\frac{7}{13} = 18.53846153846154$$