Issolvi sqrt{18^2+(144/sqrt{3})^2}=

$$\sqrt { 18 ^ { 2 } + ( \frac { 144 } { \sqrt { 3 } } ) ^ { 2 } } =$$

Evalwa

$$6\sqrt{201}\approx 85.064681273$$

Passi tas-Soluzzjonijiet

Ikkalkula 18 bil-power ta' 2 u tikseb 324.

$$\sqrt{324+\left(\frac{144}{\sqrt{3}}\right)^{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{144}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\sqrt{324+\left(\frac{144\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}}$$

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

$$\sqrt{324+\left(\frac{144\sqrt{3}}{3}\right)^{2}}$$

Iddividi 144\sqrt{3} b'3 biex tikseb48\sqrt{3}.

$$\sqrt{324+\left(48\sqrt{3}\right)^{2}}$$

Espandi \left(48\sqrt{3}\right)^{2}.

$$\sqrt{324+48^{2}\left(\sqrt{3}\right)^{2}}$$

Ikkalkula 48 bil-power ta' 2 u tikseb 2304.

$$\sqrt{324+2304\left(\sqrt{3}\right)^{2}}$$

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

$$\sqrt{324+2304\times 3}$$

Immultiplika 2304 u 3 biex tikseb 6912.

$$\sqrt{324+6912}$$

Żid 324 u 6912 biex tikseb 7236.

$$\sqrt{7236}$$

Iffattura 7236=6^{2}\times 201. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6^{2}\times 201} bħala l-prodott tal-għeruq kwadrati \sqrt{6^{2}}\sqrt{201}. Ħu l-għerq kwadrat ta' 6^{2}.

$$6\sqrt{201}$$