Datrys frac{3+2sqrt{2}}{2+sqrt{2}}*frac{sqrt{2}-1}{sqrt{2}}

$$\frac { 3 + 2 \sqrt { 2 } } { 2 + \sqrt { 2 } } \cdot \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } }$$

Enrhifo

$$\frac{1}{2}=0.5$$

Camau Ateb

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

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

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

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2^{2}-\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

Sgwâr 2. Sgwâr \sqrt{2}.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{4-2}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

Tynnu 2 o 4 i gael 2.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\sqrt{2}-1}{\sqrt{2}}$$

Mae'n rhesymoli enwadur \frac{\sqrt{2}-1}{\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{2} yw 2.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2}\times \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{2}$$

Lluoswch \frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}{2} â \frac{\left(\sqrt{2}-1\right)\sqrt{2}}{2} drwy luosi'r rhifiadur â’r rhifiadur a'r enwadur â’r enwadur.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{2\times 2}$$

Lluosi 2 a 2 i gael 4.

$$\frac{\left(3+2\sqrt{2}\right)\left(2-\sqrt{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

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

$$\frac{\left(6-3\sqrt{2}+4\sqrt{2}-2\left(\sqrt{2}\right)^{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

Cyfuno -3\sqrt{2} a 4\sqrt{2} i gael \sqrt{2}.

$$\frac{\left(6+\sqrt{2}-2\left(\sqrt{2}\right)^{2}\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

Sgwâr \sqrt{2} yw 2.

$$\frac{\left(6+\sqrt{2}-2\times 2\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

Lluosi -2 a 2 i gael -4.

$$\frac{\left(6+\sqrt{2}-4\right)\left(\sqrt{2}-1\right)\sqrt{2}}{4}$$

Tynnu 4 o 6 i gael 2.

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

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 2+\sqrt{2} gan bob \sqrt{2}-1.

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

Sgwâr \sqrt{2} yw 2.

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

Adio -2 a 2 i gael 0.

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

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

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

Lluosi \sqrt{2} a \sqrt{2} i gael 2.

$$\frac{2}{4}$$

Lleihau'r ffracsiwn \frac{2}{4} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$\frac{1}{2}$$

Ffactor

$$\frac{1}{2} = 0.5$$