Datrys sqrt{31/5}divsqrt{13/5}

$$\sqrt { 3 \frac { 1 } { 5 } } \div \sqrt { 1 \frac { 3 } { 5 } }$$

Enrhifo

$$\sqrt{2}\approx 1.414213562$$

Camau Ateb

Lluosi 3 a 5 i gael 15.

$$\frac{\sqrt{\frac{15+1}{5}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Adio 15 a 1 i gael 16.

$$\frac{\sqrt{\frac{16}{5}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{16}{5}} fel rhaniad ail israddau \frac{\sqrt{16}}{\sqrt{5}}.

$$\frac{\frac{\sqrt{16}}{\sqrt{5}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Cyfrifo ail isradd 16 a chael 4.

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

Mae'n rhesymoli enwadur \frac{4}{\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{5}.

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

Sgwâr \sqrt{5} yw 5.

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

Lluosi 1 a 5 i gael 5.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{5+3}{5}}}$$

Adio 5 a 3 i gael 8.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{8}{5}}}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{8}{5}} fel rhaniad ail israddau \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\frac{4\sqrt{5}}{5}}{\frac{\sqrt{8}}{\sqrt{5}}}$$

Ffactora 8=2^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 2} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{2}. Cymryd isradd 2^{2}.

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

Mae'n rhesymoli enwadur \frac{2\sqrt{2}}{\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{5}.

$$\frac{\frac{4\sqrt{5}}{5}}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

Sgwâr \sqrt{5} yw 5.

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

I luosi \sqrt{2} a \sqrt{5}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{\frac{4\sqrt{5}}{5}}{\frac{2\sqrt{10}}{5}}$$

Rhannwch \frac{4\sqrt{5}}{5} â \frac{2\sqrt{10}}{5} drwy luosi \frac{4\sqrt{5}}{5} â chilydd \frac{2\sqrt{10}}{5}.

$$\frac{4\sqrt{5}\times 5}{5\times 2\sqrt{10}}$$

Canslo 2\times 5 yn y rhifiadur a'r enwadur.

$$\frac{2\sqrt{5}}{\sqrt{10}}$$

Mae'n rhesymoli enwadur \frac{2\sqrt{5}}{\sqrt{10}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{10}.

$$\frac{2\sqrt{5}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

Sgwâr \sqrt{10} yw 10.

$$\frac{2\sqrt{5}\sqrt{10}}{10}$$

Ffactora 10=5\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{5\times 2} fel lluoswm ail israddau \sqrt{5}\sqrt{2}.

$$\frac{2\sqrt{5}\sqrt{5}\sqrt{2}}{10}$$

Lluosi \sqrt{5} a \sqrt{5} i gael 5.

$$\frac{2\times 5\sqrt{2}}{10}$$

Lluosi 2 a 5 i gael 10.

$$\frac{10\sqrt{2}}{10}$$

Canslo 10 a 10.

$$\sqrt{2}$$