Réitigh (3+sqrt{2})^2-4(2-sqrt{2})

$$( 3 + \sqrt { 2 } ) ^ { 2 } - 4 ( 2 - \sqrt { 2 } )$$

Luacháil

$$10\sqrt{2}+3\approx 17.142135624$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(3+\sqrt{2}\right)^{2} a leathnú.

$$9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}-4\left(2-\sqrt{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$9+6\sqrt{2}+2-4\left(2-\sqrt{2}\right)$$

Suimigh 9 agus 2 chun 11 a fháil.

$$11+6\sqrt{2}-4\left(2-\sqrt{2}\right)$$

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

$$11+6\sqrt{2}-8+4\sqrt{2}$$

Dealaigh 8 ó 11 chun 3 a fháil.

$$3+6\sqrt{2}+4\sqrt{2}$$

Comhcheangail 6\sqrt{2} agus 4\sqrt{2} chun 10\sqrt{2} a fháil.

$$3+10\sqrt{2}$$