Issolvi sqrt{(2sqrt{15})^2+(4sqrt{5})^2}

$$\sqrt { ( 2 \sqrt { 15 } ) ^ { 2 } + ( 4 \sqrt { 5 } ) ^ { 2 } }$$

Evalwa

$$2\sqrt{35}\approx 11.832159566$$

Passi tas-Soluzzjonijiet

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

$$\sqrt{2^{2}\left(\sqrt{15}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

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

$$\sqrt{4\left(\sqrt{15}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

Il-kwadrat ta' \sqrt{15} huwa 15.

$$\sqrt{4\times 15+\left(4\sqrt{5}\right)^{2}}$$

Immultiplika 4 u 15 biex tikseb 60.

$$\sqrt{60+\left(4\sqrt{5}\right)^{2}}$$

Espandi \left(4\sqrt{5}\right)^{2}.

$$\sqrt{60+4^{2}\left(\sqrt{5}\right)^{2}}$$

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

$$\sqrt{60+16\left(\sqrt{5}\right)^{2}}$$

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

$$\sqrt{60+16\times 5}$$

Immultiplika 16 u 5 biex tikseb 80.

$$\sqrt{60+80}$$

Żid 60 u 80 biex tikseb 140.

$$\sqrt{140}$$

Iffattura 140=2^{2}\times 35. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 35} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{35}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\sqrt{35}$$