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

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

Luacháil

$$5-3\sqrt{2}\approx 0.757359313$$

Céimeanna Réitigh

Úsáid an t-airí dáileach chun \sqrt{2} a mhéadú faoi 4-\sqrt{2}.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Úsáid an t-airí dáileach chun 2 a mhéadú faoi \sqrt{2}+1.

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

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

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

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

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

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

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

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 4 agus 2 chun 8 a fháil.

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

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Dealaigh 4 ó 8 chun 4 a fháil.

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

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

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

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{8\times 2-8\sqrt{2}-4\sqrt{2}+4}{4}$$

Méadaigh 8 agus 2 chun 16 a fháil.

$$\frac{16-8\sqrt{2}-4\sqrt{2}+4}{4}$$

Comhcheangail -8\sqrt{2} agus -4\sqrt{2} chun -12\sqrt{2} a fháil.

$$\frac{16-12\sqrt{2}+4}{4}$$

Suimigh 16 agus 4 chun 20 a fháil.

$$\frac{20-12\sqrt{2}}{4}$$

Roinn 20-12\sqrt{2} faoi 4 chun 5-3\sqrt{2} a fháil.

$$5-3\sqrt{2}$$