Issolvi 2sqrt{3}divsqrt{3}+4sqrt{15}divsqrt{3}

$$2 \sqrt { 3 } \div \sqrt { 3 } + 4 \sqrt { 15 } \div \sqrt { 3 }$$

Evalwa

$$4\sqrt{5}+2\approx 10.94427191$$

Passi tas-Soluzzjonijiet

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

$$\frac{2\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{4\sqrt{15}}{\sqrt{3}}$$

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

$$\frac{2\sqrt{3}\sqrt{3}}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

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

$$\frac{2\times 3}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

Iddividi 6 b'3 biex tikseb2.

$$2+\frac{4\sqrt{15}}{\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{4\sqrt{15}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$2+\frac{4\sqrt{15}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

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

$$2+\frac{4\sqrt{15}\sqrt{3}}{3}$$

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}.

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

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

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

Annulla 3 u 3.

$$2+4\sqrt{5}$$

Fattur

$$2 {(2 \sqrt{5} + 1)} = 10.94427191$$