Réitigh frac{2+sqrt{2}}{3+sqrt{2}}

$$\frac { 2 + \sqrt { 2 } } { 3 + \sqrt { 2 } }$$

Luacháil

$$\frac{\sqrt{2}+4}{7}\approx 0.77345908$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 3-\sqrt{2} chun ainmneoir \frac{2+\sqrt{2}}{3+\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(3+\sqrt{2}\right)\left(3-\sqrt{2}\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}.

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

Cearnóg 3. Cearnóg \sqrt{2}.

$$\frac{\left(2+\sqrt{2}\right)\left(3-\sqrt{2}\right)}{9-2}$$

Dealaigh 2 ó 9 chun 7 a fháil.

$$\frac{\left(2+\sqrt{2}\right)\left(3-\sqrt{2}\right)}{7}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 2+\sqrt{2} a iolrú faoi gach téarma de 3-\sqrt{2}.

$$\frac{6-2\sqrt{2}+3\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

Comhcheangail -2\sqrt{2} agus 3\sqrt{2} chun \sqrt{2} a fháil.

$$\frac{6+\sqrt{2}-\left(\sqrt{2}\right)^{2}}{7}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{6+\sqrt{2}-2}{7}$$

Dealaigh 2 ó 6 chun 4 a fháil.

$$\frac{4+\sqrt{2}}{7}$$

Fachtóirigh

$$\frac{\sqrt{2} + 4}{7} = 0.7734590803390136$$