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

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

Enrhifo

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Camau Ateb

Ffactora 12=2^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 3} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{3}. Cymryd isradd 2^{2}.

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

Ffactora 50=5^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 2} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{2}. Cymryd isradd 5^{2}.

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

Lluosi 3 a 5 i gael 15.

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

Ffactora 162=9^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{9^{2}\times 2} fel lluoswm ail israddau \sqrt{9^{2}}\sqrt{2}. Cymryd isradd 9^{2}.

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

Cyfuno 15\sqrt{2} a -9\sqrt{2} i gael 6\sqrt{2}.

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

Lluosi 2 a 6 i gael 12.

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

I luosi \sqrt{3} a \sqrt{2}, dylid lluosi'r rhifau dan yr ail isradd.

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

Ffactora 18=3^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 2} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{2}. Cymryd isradd 3^{2}.

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

Ffactora 432=12^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{12^{2}\times 3} fel lluoswm ail israddau \sqrt{12^{2}}\sqrt{3}. Cymryd isradd 12^{2}.

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

Ffactora 192=8^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{8^{2}\times 3} fel lluoswm ail israddau \sqrt{8^{2}}\sqrt{3}. Cymryd isradd 8^{2}.

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

Cyfuno 12\sqrt{3} a -8\sqrt{3} i gael 4\sqrt{3}.

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

Lluosi 3 a 4 i gael 12.

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

I luosi \sqrt{2} a \sqrt{3}, dylid lluosi'r rhifau dan yr ail isradd.

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

Cyfuno 12\sqrt{6} a -12\sqrt{6} i gael 0.

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Ffactor

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