Issolvi (sqrt{18}-sqrt{12}+sqrt{2})*2sqrt{6}

$$( \sqrt { 18 } - \sqrt { 12 } + \sqrt { 2 } ) \times 2 \sqrt { 6 }$$

Evalwa

$$16\sqrt{3}-12\sqrt{2}\approx 10.742250173$$

Passi tas-Soluzzjonijiet

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}.

$$2\left(3\sqrt{2}-\sqrt{12}+\sqrt{2}\right)\sqrt{6}$$

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}.

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

Ikkombina 3\sqrt{2} u \sqrt{2} biex tikseb 4\sqrt{2}.

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

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

$$\left(8\sqrt{2}-4\sqrt{3}\right)\sqrt{6}$$

Uża l-propjetà distributtiva biex timmultiplika 8\sqrt{2}-4\sqrt{3} b'\sqrt{6}.

$$8\sqrt{2}\sqrt{6}-4\sqrt{3}\sqrt{6}$$

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

$$8\sqrt{2}\sqrt{2}\sqrt{3}-4\sqrt{3}\sqrt{6}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$8\times 2\sqrt{3}-4\sqrt{3}\sqrt{6}$$

Immultiplika 8 u 2 biex tikseb 16.

$$16\sqrt{3}-4\sqrt{3}\sqrt{6}$$

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}.

$$16\sqrt{3}-4\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$16\sqrt{3}-4\times 3\sqrt{2}$$

Immultiplika -4 u 3 biex tikseb -12.

$$16\sqrt{3}-12\sqrt{2}$$