Issolvi (2sqrt{3}-sqrt{6})*sqrt{12}

$$( 2 \sqrt { 3 } - \sqrt { 6 } ) \times \sqrt { 12 }$$

Evalwa

$$12-6\sqrt{2}\approx 3.514718626$$

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}.

$$\left(2\sqrt{3}-\sqrt{6}\right)\times 2\sqrt{3}$$

Uża l-propjetà distributtiva biex timmultiplika 2\sqrt{3}-\sqrt{6} b'2.

$$\left(4\sqrt{3}-2\sqrt{6}\right)\sqrt{3}$$

Uża l-propjetà distributtiva biex timmultiplika 4\sqrt{3}-2\sqrt{6} b'\sqrt{3}.

$$4\left(\sqrt{3}\right)^{2}-2\sqrt{6}\sqrt{3}$$

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

$$4\times 3-2\sqrt{6}\sqrt{3}$$

Immultiplika 4 u 3 biex tikseb 12.

$$12-2\sqrt{6}\sqrt{3}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

$$12-2\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$12-2\times 3\sqrt{2}$$

Immultiplika -2 u 3 biex tikseb -6.

$$12-6\sqrt{2}$$