Issolvi frac{6sqrt{5}}{sqrt{30}}+sqrt{150}=

$$\frac { 6 \sqrt { 5 } } { \sqrt { 30 } } + \sqrt { 150 } =$$

Evalwa

$$6\sqrt{6}\approx 14.696938457$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{6\sqrt{5}}{\sqrt{30}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{30}.

$$\frac{6\sqrt{5}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}+\sqrt{150}$$

Il-kwadrat ta' \sqrt{30} huwa 30.

$$\frac{6\sqrt{5}\sqrt{30}}{30}+\sqrt{150}$$

Iffattura 30=5\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{5}\sqrt{6}.

$$\frac{6\sqrt{5}\sqrt{5}\sqrt{6}}{30}+\sqrt{150}$$

Immultiplika \sqrt{5} u \sqrt{5} biex tikseb 5.

$$\frac{6\times 5\sqrt{6}}{30}+\sqrt{150}$$

Immultiplika 6 u 5 biex tikseb 30.

$$\frac{30\sqrt{6}}{30}+\sqrt{150}$$

Annulla 30 u 30.

$$\sqrt{6}+\sqrt{150}$$

Iffattura 150=5^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\sqrt{6}+5\sqrt{6}$$

Ikkombina \sqrt{6} u 5\sqrt{6} biex tikseb 6\sqrt{6}.

$$6\sqrt{6}$$