Réitigh (2+sqrt{3})^2-frac{sqrt{3}+sqrt{2}}{sqrt{3}-sqrt{2}}

$$( 2 + \sqrt { 3 } ) ^ { 2 } - \frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$$

Luacháil

$$4\sqrt{3}+2-2\sqrt{6}\approx 4.029223745$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(2+\sqrt{3}\right)^{2} a leathnú.

$$4+4\sqrt{3}+\left(\sqrt{3}\right)^{2}-\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$4+4\sqrt{3}+3-\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$

Suimigh 4 agus 3 chun 7 a fháil.

$$7+4\sqrt{3}-\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3}+\sqrt{2} chun ainmneoir \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}} a thiontú in uimhir chóimheasta.

$$7+4\sqrt{3}-\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}$$

Mar shampla \left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$7+4\sqrt{3}-\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Cearnóg \sqrt{3}. Cearnóg \sqrt{2}.

$$7+4\sqrt{3}-\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{3-2}$$

Dealaigh 2 ó 3 chun 1 a fháil.

$$7+4\sqrt{3}-\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{1}$$

Tugann aon rud a roinntear ar a haon é féin.

$$7+4\sqrt{3}-\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)$$

Méadaigh \sqrt{3}+\sqrt{2} agus \sqrt{3}+\sqrt{2} chun \left(\sqrt{3}+\sqrt{2}\right)^{2} a fháil.

$$7+4\sqrt{3}-\left(\sqrt{3}+\sqrt{2}\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{3}+\sqrt{2}\right)^{2} a leathnú.

$$7+4\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}+2\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 3 uimhir chearnach \sqrt{3}.

$$7+4\sqrt{3}-\left(3+2\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

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

$$7+4\sqrt{3}-\left(3+2\sqrt{6}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$7+4\sqrt{3}-\left(3+2\sqrt{6}+2\right)$$

Suimigh 3 agus 2 chun 5 a fháil.

$$7+4\sqrt{3}-\left(5+2\sqrt{6}\right)$$

Chun an mhalairt ar 5+2\sqrt{6} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$7+4\sqrt{3}-5-2\sqrt{6}$$

Dealaigh 5 ó 7 chun 2 a fháil.

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