Datrys frac{sqrt{5}div[sqrt{8}+sqrt{5}]}{sqrt{8}-sqrt{5}}

$$\frac { \sqrt { 5 } \div [ \sqrt { 8 } + \sqrt { 5 } ] } { \sqrt { 8 } - \sqrt { 5 } }$$

Enrhifo

$$\frac{\sqrt{5}}{3}\approx 0.745355992$$

Camau Ateb

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}.

$$\frac{\frac{\sqrt{5}}{2\sqrt{2}+\sqrt{5}}}{\sqrt{8}-\sqrt{5}}$$

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

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{\left(2\sqrt{2}+\sqrt{5}\right)\left(2\sqrt{2}-\sqrt{5}\right)}}{\sqrt{8}-\sqrt{5}}$$

Ystyriwch \left(2\sqrt{2}+\sqrt{5}\right)\left(2\sqrt{2}-\sqrt{5}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{\left(2\sqrt{2}\right)^{2}-\left(\sqrt{5}\right)^{2}}}{\sqrt{8}-\sqrt{5}}$$

Ehangu \left(2\sqrt{2}\right)^{2}.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{2^{2}\left(\sqrt{2}\right)^{2}-\left(\sqrt{5}\right)^{2}}}{\sqrt{8}-\sqrt{5}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

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

Sgwâr \sqrt{2} yw 2.

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

Lluosi 4 a 2 i gael 8.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{8-\left(\sqrt{5}\right)^{2}}}{\sqrt{8}-\sqrt{5}}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{8-5}}{\sqrt{8}-\sqrt{5}}$$

Tynnu 5 o 8 i gael 3.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{3}}{\sqrt{8}-\sqrt{5}}$$

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}.

$$\frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{3}}{2\sqrt{2}-\sqrt{5}}$$

Mynegwch \frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{3}}{2\sqrt{2}-\sqrt{5}} fel ffracsiwn unigol.

$$\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{3\left(2\sqrt{2}-\sqrt{5}\right)}$$

Canslo -\sqrt{5}+2\sqrt{2} yn y rhifiadur a'r enwadur.

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