Datrys frac{2+sqrt{2}}{3+sqrt{2}}

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

Enrhifo

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

Camau Ateb

Mae'n rhesymoli enwadur \frac{2+\sqrt{2}}{3+\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â 3-\sqrt{2}.

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

Ystyriwch \left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Sgwâr 3. Sgwâr \sqrt{2}.

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

Tynnu 2 o 9 i gael 7.

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

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 2+\sqrt{2} gan bob 3-\sqrt{2}.

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

Cyfuno -2\sqrt{2} a 3\sqrt{2} i gael \sqrt{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Tynnu 2 o 6 i gael 4.

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

Ffactor

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