Datrys (2sqrt{8}-3sqrt{3}+5sqrt{32})-(3sqrt{27}-6sqrt{24})

$$( 2 \sqrt { 8 } - 3 \sqrt { 3 } + 5 \sqrt { 32 } ) - ( 3 \sqrt { 27 } - 6 \sqrt { 24 } )$$

Enrhifo

$$12\left(\sqrt{6}+2\sqrt{2}-\sqrt{3}\right)\approx 42.55039272$$

Camau Ateb

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

$$2\times 2\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Lluosi 2 a 2 i gael 4.

$$4\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Ffactora 32=4^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{4^{2}\times 2} fel lluoswm ail israddau \sqrt{4^{2}}\sqrt{2}. Cymryd isradd 4^{2}.

$$4\sqrt{2}-3\sqrt{3}+5\times 4\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Lluosi 5 a 4 i gael 20.

$$4\sqrt{2}-3\sqrt{3}+20\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Cyfuno 4\sqrt{2} a 20\sqrt{2} i gael 24\sqrt{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Ffactora 27=3^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 3} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{3}. Cymryd isradd 3^{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\times 3\sqrt{3}-6\sqrt{24}\right)$$

Lluosi 3 a 3 i gael 9.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\sqrt{24}\right)$$

Ffactora 24=2^{2}\times 6. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 6} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{6}. Cymryd isradd 2^{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\times 2\sqrt{6}\right)$$

Lluosi -6 a 2 i gael -12.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-12\sqrt{6}\right)$$

I ddod o hyd i wrthwyneb 9\sqrt{3}-12\sqrt{6}, dewch o hyd i wrthwyneb pob term.

$$24\sqrt{2}-3\sqrt{3}-9\sqrt{3}-\left(-12\sqrt{6}\right)$$

Cyfuno -3\sqrt{3} a -9\sqrt{3} i gael -12\sqrt{3}.

$$24\sqrt{2}-12\sqrt{3}-\left(-12\sqrt{6}\right)$$

Gwrthwyneb -12\sqrt{6} yw 12\sqrt{6}.

$$24\sqrt{2}-12\sqrt{3}+12\sqrt{6}$$