Réitigh frac{sqrt{2}+4}{sqrt{2}-1}

$$\frac{ \sqrt{ 2 } +4 }{ \sqrt{ 2 } -1 }$$

Luacháil

$$5\sqrt{2}+6\approx 13.071067812$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}+1 chun ainmneoir \frac{\sqrt{2}+4}{\sqrt{2}-1} a thiontú in uimhir chóimheasta.

$$\frac{\left(\sqrt{2}+4\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}$$

Mar shampla \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\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}.

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

Cearnóg \sqrt{2}. Cearnóg 1.

$$\frac{\left(\sqrt{2}+4\right)\left(\sqrt{2}+1\right)}{2-1}$$

Dealaigh 1 ó 2 chun 1 a fháil.

$$\frac{\left(\sqrt{2}+4\right)\left(\sqrt{2}+1\right)}{1}$$

Tugann aon rud a roinntear ar a haon é féin.

$$\left(\sqrt{2}+4\right)\left(\sqrt{2}+1\right)$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de \sqrt{2}+4 a iolrú faoi gach téarma de \sqrt{2}+1.

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

Is é 2 uimhir chearnach \sqrt{2}.

$$2+\sqrt{2}+4\sqrt{2}+4$$

Comhcheangail \sqrt{2} agus 4\sqrt{2} chun 5\sqrt{2} a fháil.

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

Suimigh 2 agus 4 chun 6 a fháil.

$$6+5\sqrt{2}$$