Issolvi 2sqrt{12}+4sqrt{18}divsqrt{3}

$$2 \sqrt{ 12 } +4 \sqrt{ 18 } \div \sqrt{ 3 }$$

Evalwa

$$4\left(\sqrt{3}+\sqrt{6}\right)\approx 16.726162201$$

Passi tas-Soluzzjonijiet

Iffattura 12=2^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 2^{2}.

$$2\times 2\sqrt{3}+\frac{4\sqrt{18}}{\sqrt{3}}$$

Immultiplika 2 u 2 biex tikseb 4.

$$4\sqrt{3}+\frac{4\sqrt{18}}{\sqrt{3}}$$

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$4\sqrt{3}+\frac{4\times 3\sqrt{2}}{\sqrt{3}}$$

Immultiplika 4 u 3 biex tikseb 12.

$$4\sqrt{3}+\frac{12\sqrt{2}}{\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{12\sqrt{2}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$4\sqrt{3}+\frac{12\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

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

$$4\sqrt{3}+\frac{12\sqrt{2}\sqrt{3}}{3}$$

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

$$4\sqrt{3}+\frac{12\sqrt{6}}{3}$$

Iddividi 12\sqrt{6} b'3 biex tikseb4\sqrt{6}.

$$4\sqrt{3}+4\sqrt{6}$$

Fattur

$$4 {(\sqrt{3} + \sqrt{6})} = 16.726162201$$