Réitigh sqrt{50}-1/sqrt{5}+2sqrt{20}-sqrt{45}+frac{sqrt{2}}{}2

$$\sqrt{ 50 } - \frac{ 1 }{ \sqrt{ 5 } } +2 \sqrt{ 20 } - \sqrt{ 45 } + \frac{ \sqrt{ 2 } }{ } 2$$

Luacháil

$$\frac{4\sqrt{5}}{5}+7\sqrt{2}\approx 11.688349319$$

Céimeanna Réitigh

Fachtóirigh 50=5^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{5^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{5^{2}}\sqrt{2}. Tóg fréamh chearnach 5^{2}.

$$5\sqrt{2}-\frac{1}{\sqrt{5}}+2\sqrt{20}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{5} chun ainmneoir \frac{1}{\sqrt{5}} a thiontú in uimhir chóimheasta.

$$5\sqrt{2}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+2\sqrt{20}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$5\sqrt{2}-\frac{\sqrt{5}}{5}+2\sqrt{20}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Fachtóirigh 20=2^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{5}. Tóg fréamh chearnach 2^{2}.

$$5\sqrt{2}-\frac{\sqrt{5}}{5}+2\times 2\sqrt{5}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$5\sqrt{2}-\frac{\sqrt{5}}{5}+4\sqrt{5}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Comhcheangail -\frac{\sqrt{5}}{5} agus 4\sqrt{5} chun \frac{19}{5}\sqrt{5} a fháil.

$$5\sqrt{2}+\frac{19}{5}\sqrt{5}-\sqrt{45}+2\times \frac{\sqrt{2}}{1}$$

Fachtóirigh 45=3^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{5}. Tóg fréamh chearnach 3^{2}.

$$5\sqrt{2}+\frac{19}{5}\sqrt{5}-3\sqrt{5}+2\times \frac{\sqrt{2}}{1}$$

Comhcheangail \frac{19}{5}\sqrt{5} agus -3\sqrt{5} chun \frac{4}{5}\sqrt{5} a fháil.

$$5\sqrt{2}+\frac{4}{5}\sqrt{5}+2\times \frac{\sqrt{2}}{1}$$

Tugann aon rud a roinntear ar a haon é féin.

$$5\sqrt{2}+\frac{4}{5}\sqrt{5}+2\sqrt{2}$$

Comhcheangail 5\sqrt{2} agus 2\sqrt{2} chun 7\sqrt{2} a fháil.

$$7\sqrt{2}+\frac{4}{5}\sqrt{5}$$