Réitigh 3sqrt{22/3}div1/2sqrt{2/5}-1/8sqrt{15}

$$3 \sqrt{ 2 \frac{ 2 }{ 3 } } \div \frac{ 1 }{ 2 } \sqrt{ \frac{ 2 }{ 5 } } - \frac{ 1 }{ 8 } \sqrt{ 15 }$$

Luacháil

$$\frac{59\sqrt{15}}{40}\approx 5.712650436$$

Céimeanna Réitigh

Méadaigh 2 agus 3 chun 6 a fháil.

$$\frac{3\sqrt{\frac{6+2}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Suimigh 6 agus 2 chun 8 a fháil.

$$\frac{3\sqrt{\frac{8}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{8}{3}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{3\times \frac{\sqrt{8}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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}.

$$\frac{3\times \frac{2\sqrt{2}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Cealaigh 3 agus 3.

$$\frac{2\sqrt{6}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Roinn 2\sqrt{6} faoi \frac{1}{2} trí 2\sqrt{6} a mhéadú faoi dheilín \frac{1}{2}.

$$2\sqrt{6}\times 2\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$4\sqrt{6}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{2}{5}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{2}}{\sqrt{5}}.

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}-\frac{1}{8}\sqrt{15}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{5} chun ainmneoir \frac{\sqrt{2}}{\sqrt{5}} a thiontú in uimhir chóimheasta.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{1}{8}\sqrt{15}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}-\frac{1}{8}\sqrt{15}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{5} a iolrú.

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}-\frac{1}{8}\sqrt{15}$$

Scríobh 4\times \frac{\sqrt{10}}{5} mar chodán aonair.

$$\frac{4\sqrt{10}}{5}\sqrt{6}-\frac{1}{8}\sqrt{15}$$

Scríobh \frac{4\sqrt{10}}{5}\sqrt{6} mar chodán aonair.

$$\frac{4\sqrt{10}\sqrt{6}}{5}-\frac{1}{8}\sqrt{15}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{10} agus \sqrt{6} a iolrú.

$$\frac{4\sqrt{60}}{5}-\frac{1}{8}\sqrt{15}$$

Fachtóirigh 60=2^{2}\times 15. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 15} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{15}. Tóg fréamh chearnach 2^{2}.

$$\frac{4\times 2\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Méadaigh 4 agus 2 chun 8 a fháil.

$$\frac{8\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Comhcheangail \frac{8\sqrt{15}}{5} agus -\frac{1}{8}\sqrt{15} chun \frac{59}{40}\sqrt{15} a fháil.

$$\frac{59}{40}\sqrt{15}$$