Issolvi 2/sqrt{5}+sqrt{20}+8/sqrt{80}

$$\frac { 2 } { \sqrt { 5 } } + \sqrt { 20 } + \frac { 8 } { \sqrt { 80 } }$$

Evalwa

$$\frac{14\sqrt{5}}{5}\approx 6.260990337$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{2}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\sqrt{20}+\frac{8}{\sqrt{80}}$$

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

$$\frac{2\sqrt{5}}{5}+\sqrt{20}+\frac{8}{\sqrt{80}}$$

Iffattura 20=2^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{2\sqrt{5}}{5}+2\sqrt{5}+\frac{8}{\sqrt{80}}$$

Ikkombina \frac{2\sqrt{5}}{5} u 2\sqrt{5} biex tikseb \frac{12}{5}\sqrt{5}.

$$\frac{12}{5}\sqrt{5}+\frac{8}{\sqrt{80}}$$

Iffattura 80=4^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 4^{2}.

$$\frac{12}{5}\sqrt{5}+\frac{8}{4\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{8}{4\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{12}{5}\sqrt{5}+\frac{8\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{12}{5}\sqrt{5}+\frac{8\sqrt{5}}{4\times 5}$$

Annulla 4 fin-numeratur u d-denominatur.

$$\frac{12}{5}\sqrt{5}+\frac{2\sqrt{5}}{5}$$

Ikkombina \frac{12}{5}\sqrt{5} u \frac{2\sqrt{5}}{5} biex tikseb \frac{14}{5}\sqrt{5}.

$$\frac{14}{5}\sqrt{5}$$