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

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

Luacháil

$$\frac{7\sqrt{3}}{3}\approx 4.041451884$$

Céimeanna gearra réitigh

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}.

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

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}.

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

Cealaigh 3 agus 3.

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

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

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

Áirigh fréamh chearnach 4 agus faigh 2.

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

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

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

Is é 3 uimhir chearnach \sqrt{3}.

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

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

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

Áirigh fréamh chearnach 1 agus faigh 1.

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

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

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Cealaigh an comhfhachtóir 2 is mó in 4 agus 2.

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

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

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

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

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

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

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

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

$$\frac{3\left(3\sqrt{3}-2\sqrt{2}\right)}{3}-\frac{2\sqrt{3}-6\sqrt{2}}{3}$$

Tá an t-ainmneoir céanna ag \frac{3\left(3\sqrt{3}-2\sqrt{2}\right)}{3} agus \frac{2\sqrt{3}-6\sqrt{2}}{3} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{3\left(3\sqrt{3}-2\sqrt{2}\right)-\left(2\sqrt{3}-6\sqrt{2}\right)}{3}$$

Déan iolrúcháin in 3\left(3\sqrt{3}-2\sqrt{2}\right)-\left(2\sqrt{3}-6\sqrt{2}\right).

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

Déan áirimh in 9\sqrt{3}-6\sqrt{2}-2\sqrt{3}+6\sqrt{2}.

$$\frac{7\sqrt{3}}{3}$$