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

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

Luacháil

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

Céimeanna Réitigh

Fachtóirigh 8=2^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{2}. Tóg fréamh chearnach 2^{2}.

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

Méadaigh 2 agus 2 chun 4 a fháil.

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

Fachtóirigh 32=4^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{2}. Tóg fréamh chearnach 4^{2}.

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

Méadaigh 5 agus 4 chun 20 a fháil.

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

Comhcheangail 4\sqrt{2} agus 20\sqrt{2} chun 24\sqrt{2} a fháil.

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

Fachtóirigh 27=3^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{3}. Tóg fréamh chearnach 3^{2}.

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

Méadaigh 3 agus 3 chun 9 a fháil.

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

Fachtóirigh 24=2^{2}\times 6. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 6} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{6}. Tóg fréamh chearnach 2^{2}.

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

Méadaigh -6 agus 2 chun -12 a fháil.

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

Chun an mhalairt ar 9\sqrt{3}-12\sqrt{6} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail -3\sqrt{3} agus -9\sqrt{3} chun -12\sqrt{3} a fháil.

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

Tá 12\sqrt{6} urchomhairleach le -12\sqrt{6}.

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