Réitigh 2sqrt{1/27}-2/3sqrt{18}-sqrt{4/3}-4sqrt{1/2}

$$2 \sqrt{ \frac{ 1 }{ 27 } } - \frac{ 2 }{ 3 } \sqrt{ 18 } - \sqrt{ \frac{ 4 }{ 3 } } -4 \sqrt{ \frac{ 1 }{ 2 } }$$

Luacháil

$$-\frac{4\sqrt{3}}{9}-4\sqrt{2}\approx -6.426654608$$

Céimeanna gearra réitigh

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{27}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{27}}.

$$2\times \frac{\sqrt{1}}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Áirigh fréamh chearnach 1 agus faigh 1.

$$2\times \frac{1}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

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}.

$$2\times \frac{1}{3\sqrt{3}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3} chun ainmneoir \frac{1}{3\sqrt{3}} a thiontú in uimhir chóimheasta.

$$2\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$2\times \frac{\sqrt{3}}{3\times 3}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Méadaigh 3 agus 3 chun 9 a fháil.

$$2\times \frac{\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Scríobh 2\times \frac{\sqrt{3}}{9} mar chodán aonair.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Fachtóirigh 18=3^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{2}. Tóg fréamh chearnach 3^{2}.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\times 3\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Cealaigh 3 agus 3.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{4}{3}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{\sqrt{4}}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

Áirigh fréamh chearnach 4 agus faigh 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

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

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

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\sqrt{\frac{1}{2}}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{2}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Áirigh fréamh chearnach 1 agus faigh 1.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{1}{\sqrt{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{1}{\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{2}}{2}$$

Cealaigh an comhfhachtóir 2 is mó in 4 agus 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-2\sqrt{2}$$

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

$$\frac{2\sqrt{3}}{9}-4\sqrt{2}-\frac{2\sqrt{3}}{3}$$

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

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

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

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

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

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{2\sqrt{3}}{3}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 9 agus 3 ná 9. Méadaigh \frac{2\sqrt{3}}{3} faoi \frac{3}{3}.

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{3\times 2\sqrt{3}}{9}$$

Tá an t-ainmneoir céanna ag \frac{2\sqrt{3}-36\sqrt{2}}{9} agus \frac{3\times 2\sqrt{3}}{9} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3}}{9}$$

Déan iolrúcháin in 2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3}.

$$\frac{2\sqrt{3}-36\sqrt{2}-6\sqrt{3}}{9}$$

Déan áirimh in 2\sqrt{3}-36\sqrt{2}-6\sqrt{3}.

$$\frac{-4\sqrt{3}-36\sqrt{2}}{9}$$

Fachtóirigh

$$\frac{4 {(-\sqrt{3} - 9 \sqrt{2})}}{9} = -6.426654608411882$$