Issolvi sqrt{80}+5sqrt{1/5}-3sqrt{5}+1/5sqrt{125}

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 5 } } -3 \sqrt{ 5 } + \frac{ 1 }{ 5 } \sqrt{ 125 }$$

Evalwa

$$3\sqrt{5}\approx 6.708203932$$

Passi tas-Soluzzjonijiet

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}.

$$4\sqrt{5}+5\sqrt{\frac{1}{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{5}}.

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

$$4\sqrt{5}+5\times \frac{1}{\sqrt{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Annulla 5 u 5.

$$4\sqrt{5}+\sqrt{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ikkombina 4\sqrt{5} u \sqrt{5} biex tikseb 5\sqrt{5}.

$$5\sqrt{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ikkombina 5\sqrt{5} u -3\sqrt{5} biex tikseb 2\sqrt{5}.

$$2\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Iffattura 125=5^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 5^{2}.

$$2\sqrt{5}+\frac{1}{5}\times 5\sqrt{5}$$

Annulla 5 u 5.

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

Ikkombina 2\sqrt{5} u \sqrt{5} biex tikseb 3\sqrt{5}.

$$3\sqrt{5}$$