Issolvi {r}{2sqrt{20}-sqrt{5}}{+3sqrt{1/5}}

$$\left. \begin{array} { r } { 2 \sqrt { 20 } - \sqrt { 5 } } \\ { + 3 \sqrt { \frac { 1 } { 5 } } } \end{array} \right.$$

Evalwa

$$\frac{18\sqrt{5}}{5}\approx 8.049844719$$

Passi tas-Soluzzjonijiet

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}.

$$2\times 2\sqrt{5}-\sqrt{5}+3\sqrt{\frac{1}{5}}$$

Immultiplika 2 u 2 biex tikseb 4.

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

Ikkombina 4\sqrt{5} u -\sqrt{5} biex tikseb 3\sqrt{5}.

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

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

$$3\sqrt{5}+3\times \frac{\sqrt{1}}{\sqrt{5}}$$

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

$$3\sqrt{5}+3\times \frac{1}{\sqrt{5}}$$

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

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

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

$$3\sqrt{5}+3\times \frac{\sqrt{5}}{5}$$

Esprimi 3\times \frac{\sqrt{5}}{5} bħala frazzjoni waħda.

$$3\sqrt{5}+\frac{3\sqrt{5}}{5}$$

Ikkombina 3\sqrt{5} u \frac{3\sqrt{5}}{5} biex tikseb \frac{18}{5}\sqrt{5}.

$$\frac{18}{5}\sqrt{5}$$