Réitigh (5sqrt{2}-4)^2-(3-sqrt{2})^2

$$( 5 \sqrt { 2 } - 4 ) ^ { 2 } - ( 3 - \sqrt { 2 } ) ^ { 2 }$$

Luacháil

$$55-34\sqrt{2}\approx 6.916738879$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(5\sqrt{2}-4\right)^{2} a leathnú.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Méadaigh 25 agus 2 chun 50 a fháil.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Suimigh 50 agus 16 chun 66 a fháil.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Suimigh 9 agus 2 chun 11 a fháil.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Chun an mhalairt ar 11-6\sqrt{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Dealaigh 11 ó 66 chun 55 a fháil.

$$55-40\sqrt{2}+6\sqrt{2}$$

Comhcheangail -40\sqrt{2} agus 6\sqrt{2} chun -34\sqrt{2} a fháil.

$$55-34\sqrt{2}$$

Fairsingigh

$$55-34\sqrt{2}$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(5\sqrt{2}-4\right)^{2} a leathnú.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Méadaigh 25 agus 2 chun 50 a fháil.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Suimigh 50 agus 16 chun 66 a fháil.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Suimigh 9 agus 2 chun 11 a fháil.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Chun an mhalairt ar 11-6\sqrt{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Dealaigh 11 ó 66 chun 55 a fháil.

$$55-40\sqrt{2}+6\sqrt{2}$$

Comhcheangail -40\sqrt{2} agus 6\sqrt{2} chun -34\sqrt{2} a fháil.

$$55-34\sqrt{2}$$