Réitigh (2sqrt{2}-1)^2+(2sqrt{3}-1)(-2sqrt{3}-1)+frac{sqrt{12}-3}{sqrt{3}}

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } + ( 2 \sqrt { 3 } - 1 ) ( - 2 \sqrt { 3 } - 1 ) + \frac { \sqrt { 12 } - 3 } { \sqrt { 3 } }$$

Luacháil

$$-\sqrt{3}-4\sqrt{2}\approx -7.388905057$$

Céimeanna gearra réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(2\sqrt{2}-1\right)^{2} a leathnú.

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$4\times 2-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Méadaigh 4 agus 2 chun 8 a fháil.

$$8-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Suimigh 8 agus 1 chun 9 a fháil.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Fachtóirigh 12=2^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{3}. Tóg fréamh chearnach 2^{2}.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{2\sqrt{3}-3}{\sqrt{3}}$$

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

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 9-4\sqrt{2} faoi \frac{3}{3}.

$$\frac{3\left(9-4\sqrt{2}\right)}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}$$

Tá an t-ainmneoir céanna ag \frac{3\left(9-4\sqrt{2}\right)}{3} agus \frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{3\left(9-4\sqrt{2}\right)+\left(2\sqrt{3}-3\right)\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Déan iolrúcháin in 3\left(9-4\sqrt{2}\right)+\left(2\sqrt{3}-3\right)\sqrt{3}.

$$\frac{27-12\sqrt{2}+6-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Déan áirimh in 27-12\sqrt{2}+6-3\sqrt{3}.

$$\frac{33-12\sqrt{2}-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Roinn 33-12\sqrt{2}-3\sqrt{3} faoi 3 chun 11-4\sqrt{2}-\sqrt{3} a fháil.

$$11-4\sqrt{2}-\sqrt{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Úsáid an t-airí dáileach chun 2\sqrt{3}-1 a mhéadú faoi -2\sqrt{3}-1 agus chun téarmaí comhchosúla a chumasc.

$$11-4\sqrt{2}-\sqrt{3}-4\left(\sqrt{3}\right)^{2}+1$$

Is é 3 uimhir chearnach \sqrt{3}.

$$11-4\sqrt{2}-\sqrt{3}-4\times 3+1$$

Méadaigh -4 agus 3 chun -12 a fháil.

$$11-4\sqrt{2}-\sqrt{3}-12+1$$

Suimigh -12 agus 1 chun -11 a fháil.

$$11-4\sqrt{2}-\sqrt{3}-11$$

Dealaigh 11 ó 11 chun 0 a fháil.

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