Réitigh 19*(sqrt{5}-sqrt{3}+sqrt{2})(sqrt{5}-sqrt{3}-sqrt{2})

$$19 \cdot ( \sqrt { 5 } - \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 5 } - \sqrt { 3 } - \sqrt { 2 } )$$

Luacháil

$$114-38\sqrt{15}\approx -33.173367156$$

Céimeanna Réitigh

Úsáid an t-airí dáileach chun 19 a mhéadú faoi \sqrt{5}-\sqrt{3}+\sqrt{2}.

$$\left(19\sqrt{5}-19\sqrt{3}+19\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}-\sqrt{2}\right)$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 19\sqrt{5}-19\sqrt{3}+19\sqrt{2} a iolrú faoi gach téarma de \sqrt{5}-\sqrt{3}-\sqrt{2}.

$$19\left(\sqrt{5}\right)^{2}-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$19\times 5-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Méadaigh 19 agus 5 chun 95 a fháil.

$$95-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{5} a iolrú.

$$95-19\sqrt{15}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{5} agus \sqrt{2} a iolrú.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{5} a iolrú.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{15}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Comhcheangail -19\sqrt{15} agus -19\sqrt{15} chun -38\sqrt{15} a fháil.

$$95-38\sqrt{15}-19\sqrt{10}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$95-38\sqrt{15}-19\sqrt{10}+19\times 3+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Méadaigh 19 agus 3 chun 57 a fháil.

$$95-38\sqrt{15}-19\sqrt{10}+57+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Suimigh 95 agus 57 chun 152 a fháil.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{2} a iolrú.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{5} a iolrú.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{10}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Comhcheangail -19\sqrt{10} agus 19\sqrt{10} chun 0 a fháil.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{3} agus \sqrt{2} a iolrú.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{6}-19\left(\sqrt{2}\right)^{2}$$

Comhcheangail 19\sqrt{6} agus -19\sqrt{6} chun 0 a fháil.

$$152-38\sqrt{15}-19\left(\sqrt{2}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$152-38\sqrt{15}-19\times 2$$

Méadaigh -19 agus 2 chun -38 a fháil.

$$152-38\sqrt{15}-38$$

Dealaigh 38 ó 152 chun 114 a fháil.

$$114-38\sqrt{15}$$