Réitigh 14/5sqrt{3-sqrt{5}}

$$\frac{ 14 }{ 5 \sqrt{ 3 } - \sqrt{ 5 } }$$

Luacháil

$$\frac{\sqrt{5}\left(\sqrt{15}+1\right)}{5}\approx 2.179264403$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 5\sqrt{3}+\sqrt{5} chun ainmneoir \frac{14}{5\sqrt{3}-\sqrt{5}} a thiontú in uimhir chóimheasta.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right)}$$

Mar shampla \left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\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}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Fairsingigh \left(5\sqrt{3}\right)^{2}

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Ríomh cumhacht 5 de 2 agus faigh 25.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\times 3-\left(\sqrt{5}\right)^{2}}$$

Méadaigh 25 agus 3 chun 75 a fháil.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-\left(\sqrt{5}\right)^{2}}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-5}$$

Dealaigh 5 ó 75 chun 70 a fháil.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{70}$$

Roinn 14\left(5\sqrt{3}+\sqrt{5}\right) faoi 70 chun \frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right) a fháil.

$$\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right)$$

Úsáid an t-airí dáileach chun \frac{1}{5} a mhéadú faoi 5\sqrt{3}+\sqrt{5}.

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

Cealaigh 5 agus 5.

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