Datrys sqrt{80}+5sqrt{1/5}-3sqrt{5}+1/5sqrt{125}

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 5 } } -3 \sqrt{ 5 } + \frac{ 1 }{ 5 } \sqrt{ 125 }$$

Enrhifo

$$3\sqrt{5}\approx 6.708203932$$

Camau Ateb

Ffactora 80=4^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{4^{2}\times 5} fel lluoswm ail israddau \sqrt{4^{2}}\sqrt{5}. Cymryd isradd 4^{2}.

$$4\sqrt{5}+5\sqrt{\frac{1}{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{1}{5}} fel rhaniad ail israddau \frac{\sqrt{1}}{\sqrt{5}}.

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Cyfrifo ail isradd 1 a chael 1.

$$4\sqrt{5}+5\times \frac{1}{\sqrt{5}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Mae'n rhesymoli enwadur \frac{1}{\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{5}.

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Sgwâr \sqrt{5} yw 5.

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Canslo 5 a 5.

$$4\sqrt{5}+\sqrt{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Cyfuno 4\sqrt{5} a \sqrt{5} i gael 5\sqrt{5}.

$$5\sqrt{5}-3\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Cyfuno 5\sqrt{5} a -3\sqrt{5} i gael 2\sqrt{5}.

$$2\sqrt{5}+\frac{1}{5}\sqrt{125}$$

Ffactora 125=5^{2}\times 5. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 5} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{5}. Cymryd isradd 5^{2}.

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

Canslo 5 a 5.

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

Cyfuno 2\sqrt{5} a \sqrt{5} i gael 3\sqrt{5}.

$$3\sqrt{5}$$