Issolvi sqrt{12}(3sqrt{50}-sqrt{162})-sqrt{18}(sqrt{432}-sqrt{192})

$$\sqrt { 12 } ( 3 \sqrt { 50 } - \sqrt { 162 } ) - \sqrt { 18 } ( \sqrt { 432 } - \sqrt { 192 } )$$

Evalwa

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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}.

$$2\sqrt{3}\left(3\sqrt{50}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Iffattura 50=5^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 5^{2}.

$$2\sqrt{3}\left(3\times 5\sqrt{2}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Immultiplika 3 u 5 biex tikseb 15.

$$2\sqrt{3}\left(15\sqrt{2}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Iffattura 162=9^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{9^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{9^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 9^{2}.

$$2\sqrt{3}\left(15\sqrt{2}-9\sqrt{2}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Ikkombina 15\sqrt{2} u -9\sqrt{2} biex tikseb 6\sqrt{2}.

$$2\sqrt{3}\times 6\sqrt{2}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Immultiplika 2 u 6 biex tikseb 12.

$$12\sqrt{3}\sqrt{2}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

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

$$12\sqrt{6}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

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}.

$$12\sqrt{6}-3\sqrt{2}\left(\sqrt{432}-\sqrt{192}\right)$$

Iffattura 432=12^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{12^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{12^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 12^{2}.

$$12\sqrt{6}-3\sqrt{2}\left(12\sqrt{3}-\sqrt{192}\right)$$

Iffattura 192=8^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{8^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{8^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 8^{2}.

$$12\sqrt{6}-3\sqrt{2}\left(12\sqrt{3}-8\sqrt{3}\right)$$

Ikkombina 12\sqrt{3} u -8\sqrt{3} biex tikseb 4\sqrt{3}.

$$12\sqrt{6}-3\sqrt{2}\times 4\sqrt{3}$$

Immultiplika 3 u 4 biex tikseb 12.

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

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

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

Ikkombina 12\sqrt{6} u -12\sqrt{6} biex tikseb 0.

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Fattur

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