Issolvi (sqrt{15}+2sqrt{2})divsqrt{3}

$$( \sqrt { 15 } + 2 \sqrt { 2 } ) \div \sqrt { 3 }$$

Evalwa

$$\frac{2\sqrt{6}}{3}+\sqrt{5}\approx 3.869061139$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{15}+2\sqrt{2}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{\left(\sqrt{15}+2\sqrt{2}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{\left(\sqrt{15}+2\sqrt{2}\right)\sqrt{3}}{3}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{15}+2\sqrt{2} b'\sqrt{3}.

$$\frac{\sqrt{15}\sqrt{3}+2\sqrt{2}\sqrt{3}}{3}$$

Iffattura 15=3\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{5}.

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

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

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

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{3\sqrt{5}+2\sqrt{6}}{3}$$