Réitigh sqrt{32}+sqrt{05}-2sqrt{1/3}-sqrt{1/8}+sqrt{12}-sqrt{18}

$$\sqrt{ 32 } + \sqrt{ 05 } -2 \sqrt{ \frac{ 1 }{ 3 } } - \sqrt{ \frac{ 1 }{ 8 } } + \sqrt{ 12 } - \sqrt{ 18 }$$

Luacháil

$$\frac{3\sqrt{2}}{4}+\frac{4\sqrt{3}}{3}\approx 3.370061249$$

Céimeanna gearra réitigh

Fachtóirigh 32=4^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{2}. Tóg fréamh chearnach 4^{2}.

$$4\sqrt{2}+\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Méadaigh 0 agus 5 chun 0 a fháil.

$$4\sqrt{2}+\sqrt{0}-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Áirigh fréamh chearnach 0 agus faigh 0.

$$4\sqrt{2}+0-2\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{3}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{3}}.

$$4\sqrt{2}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Áirigh fréamh chearnach 1 agus faigh 1.

$$4\sqrt{2}+0-2\times \frac{1}{\sqrt{3}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{3}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\sqrt{\frac{1}{8}}+\sqrt{12}-\sqrt{18}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{1}{8}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{8}}.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{1}}{\sqrt{8}}+\sqrt{12}-\sqrt{18}$$

Áirigh fréamh chearnach 1 agus faigh 1.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{1}{\sqrt{8}}+\sqrt{12}-\sqrt{18}$$

Fachtóirigh 8=2^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{2}. Tóg fréamh chearnach 2^{2}.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{1}{2\sqrt{2}}+\sqrt{12}-\sqrt{18}$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{12}-\sqrt{18}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{2\times 2}+\sqrt{12}-\sqrt{18}$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+\sqrt{12}-\sqrt{18}$$

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}.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+2\sqrt{3}-\sqrt{18}$$

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}.

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+2\sqrt{3}-3\sqrt{2}$$

Comhcheangail 4\sqrt{2} agus -3\sqrt{2} chun \sqrt{2} a fháil.

$$\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}+2\sqrt{3}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh \sqrt{2}+0+2\sqrt{3} faoi \frac{3}{3}.

$$\frac{3\left(\sqrt{2}+0+2\sqrt{3}\right)}{3}+\frac{-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}$$

Tá an t-ainmneoir céanna ag \frac{3\left(\sqrt{2}+0+2\sqrt{3}\right)}{3} agus \frac{-2\sqrt{3}}{3} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{3\left(\sqrt{2}+0+2\sqrt{3}\right)-2\sqrt{3}}{3}-\frac{\sqrt{2}}{4}$$

Déan iolrúcháin in 3\left(\sqrt{2}+0+2\sqrt{3}\right)-2\sqrt{3}.

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

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

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 3 agus 4 ná 12. Méadaigh \frac{3\sqrt{2}+4\sqrt{3}}{3} faoi \frac{4}{4}. Méadaigh \frac{\sqrt{2}}{4} faoi \frac{3}{3}.

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

Tá an t-ainmneoir céanna ag \frac{4\left(3\sqrt{2}+4\sqrt{3}\right)}{12} agus \frac{3\sqrt{2}}{12} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

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

$$\frac{12\sqrt{2}+16\sqrt{3}-3\sqrt{2}}{12}$$

Déan áirimh in 12\sqrt{2}+16\sqrt{3}-3\sqrt{2}.

$$\frac{9\sqrt{2}+16\sqrt{3}}{12}$$