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

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

Luacháil

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

Céimeanna Réitigh

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}.

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

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

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

Mar shampla \left(2\sqrt{2}+\sqrt{5}\right)\left(2\sqrt{2}-\sqrt{5}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Fairsingigh \left(2\sqrt{2}\right)^{2}

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

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 4 agus 2 chun 8 a fháil.

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

Is é 5 uimhir chearnach \sqrt{5}.

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

Dealaigh 5 ó 8 chun 3 a fháil.

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

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}.

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

Scríobh \frac{\frac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{3}}{2\sqrt{2}-\sqrt{5}} mar chodán aonair.

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

Cealaigh -\sqrt{5}+2\sqrt{2} mar uimhreoir agus ainmneoir.

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