Issolvi (3sqrt{6}+sqrt{30})divsqrt{6}

$$(3 \sqrt{ 6 } + \sqrt{ 30 } ) \div \sqrt{ 6 }$$

Evalwa

$$\sqrt{5}+3\approx 5.236067977$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{3\sqrt{6}+\sqrt{30}}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{6}$$

Uża l-propjetà distributtiva biex timmultiplika 3\sqrt{6}+\sqrt{30} b'\sqrt{6}.

$$\frac{3\left(\sqrt{6}\right)^{2}+\sqrt{30}\sqrt{6}}{6}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{3\times 6+\sqrt{30}\sqrt{6}}{6}$$

Immultiplika 3 u 6 biex tikseb 18.

$$\frac{18+\sqrt{30}\sqrt{6}}{6}$$

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

$$\frac{18+\sqrt{6}\sqrt{5}\sqrt{6}}{6}$$

Immultiplika \sqrt{6} u \sqrt{6} biex tikseb 6.

$$\frac{18+6\sqrt{5}}{6}$$

Iddividi kull terminu ta' 18+6\sqrt{5} b'6 biex tikseb3+\sqrt{5}.

$$3+\sqrt{5}$$