Issolvi =sqrt{2/5}+3sqrt{5}-4sqrt{5}

$$= \sqrt { \frac { 2 } { 5 } } + 3 \sqrt { 5 } - 4 \sqrt { 5 }$$

Evalwa

$$\frac{\sqrt{10}}{5}-\sqrt{5}\approx -1.603612445$$

Passi Qosra tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2}}{\sqrt{5}}.

$$\frac{\sqrt{2}}{\sqrt{5}}+3\sqrt{5}-4\sqrt{5}$$

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

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

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

$$\frac{\sqrt{2}\sqrt{5}}{5}+3\sqrt{5}-4\sqrt{5}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{10}}{5}+3\sqrt{5}-4\sqrt{5}$$

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

$$\frac{\sqrt{10}}{5}-\sqrt{5}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika \sqrt{5} b'\frac{5}{5}.

$$\frac{\sqrt{10}}{5}-\frac{5\sqrt{5}}{5}$$

Billi \frac{\sqrt{10}}{5} u \frac{5\sqrt{5}}{5} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\sqrt{10}-5\sqrt{5}}{5}$$