Issolvi frac{(sqrt{6}-sqrt{12})*sqrt{3}}{sqrt{6}}+sqrt{6}

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

Evalwa

$$\sqrt{3}\approx 1.732050808$$

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}.

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

Irrazzjonalizza d-denominatur tal-\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

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

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

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

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}.

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

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

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

Iddividi \left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2} b'6 biex tikseb\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}.

$$\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}+\sqrt{6}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{6}-2\sqrt{3} b'\frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-2\sqrt{3}\times \frac{1}{2}\right)\sqrt{2}+\sqrt{6}$$

Immultiplika -2 b'\frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-\sqrt{3}\right)\sqrt{2}+\sqrt{6}$$

Uża l-propjetà distributtiva biex timmultiplika \sqrt{6}\times \frac{1}{2}-\sqrt{3} b'\sqrt{2}.

$$\sqrt{6}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

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}.

$$\sqrt{2}\sqrt{3}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

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

$$2\times \frac{1}{2}\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Annulla 2 u 2.

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

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

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

Ikkombina -\sqrt{6} u \sqrt{6} biex tikseb 0.

$$\sqrt{3}$$