Réitigh (4sqrt{2}-3sqrt{6})(2sqrt{6}+3sqrt{2})

$$( 4 \sqrt { 2 } - 3 \sqrt { 6 } ) ( 2 \sqrt { 6 } + 3 \sqrt { 2 } )$$

Luacháil

$$-2\sqrt{3}-12\approx -15.464101615$$

Céimeanna Réitigh

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 4\sqrt{2}-3\sqrt{6} a iolrú faoi gach téarma de 2\sqrt{6}+3\sqrt{2}.

$$8\sqrt{2}\sqrt{6}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

$$8\sqrt{2}\sqrt{2}\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$8\times 2\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Méadaigh 8 agus 2 chun 16 a fháil.

$$16\sqrt{3}+12\left(\sqrt{2}\right)^{2}-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$16\sqrt{3}+12\times 2-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Méadaigh 12 agus 2 chun 24 a fháil.

$$16\sqrt{3}+24-6\left(\sqrt{6}\right)^{2}-9\sqrt{6}\sqrt{2}$$

Is é 6 uimhir chearnach \sqrt{6}.

$$16\sqrt{3}+24-6\times 6-9\sqrt{6}\sqrt{2}$$

Méadaigh -6 agus 6 chun -36 a fháil.

$$16\sqrt{3}+24-36-9\sqrt{6}\sqrt{2}$$

Dealaigh 36 ó 24 chun -12 a fháil.

$$16\sqrt{3}-12-9\sqrt{6}\sqrt{2}$$

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

$$16\sqrt{3}-12-9\sqrt{2}\sqrt{3}\sqrt{2}$$

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$16\sqrt{3}-12-9\times 2\sqrt{3}$$

Méadaigh -9 agus 2 chun -18 a fháil.

$$16\sqrt{3}-12-18\sqrt{3}$$

Comhcheangail 16\sqrt{3} agus -18\sqrt{3} chun -2\sqrt{3} a fháil.

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

Fachtóirigh

$$2 {(-\sqrt{3} - 6)} = -15.464101615$$