Datrys 1/3-sqrt{8}-2sqrt{2}+6

$$\frac { 1 } { 3 - \sqrt { 8 } } - 2 \sqrt { 2 } + 6$$

Enrhifo

$$9$$

Camau Ateb

Ffactora 8=2^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 2} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{2}. Cymryd isradd 2^{2}.

$$\frac{1}{3-2\sqrt{2}}-2\sqrt{2}+6$$

Mae'n rhesymoli enwadur \frac{1}{3-2\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â 3+2\sqrt{2}.

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

Ystyriwch \left(3-2\sqrt{2}\right)\left(3+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}.

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

Cyfrifo 3 i bŵer 2 a chael 9.

$$\frac{3+2\sqrt{2}}{9-\left(-2\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

Ehangu \left(-2\sqrt{2}\right)^{2}.

$$\frac{3+2\sqrt{2}}{9-\left(-2\right)^{2}\left(\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

Cyfrifo -2 i bŵer 2 a chael 4.

$$\frac{3+2\sqrt{2}}{9-4\left(\sqrt{2}\right)^{2}}-2\sqrt{2}+6$$

Sgwâr \sqrt{2} yw 2.

$$\frac{3+2\sqrt{2}}{9-4\times 2}-2\sqrt{2}+6$$

Lluosi 4 a 2 i gael 8.

$$\frac{3+2\sqrt{2}}{9-8}-2\sqrt{2}+6$$

Tynnu 8 o 9 i gael 1.

$$\frac{3+2\sqrt{2}}{1}-2\sqrt{2}+6$$

Mae rhannu unrhyw beth ag un yn rhoi'r rhif hwnnw.

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

Cyfuno 2\sqrt{2} a -2\sqrt{2} i gael 0.

$$3+6$$

Adio 3 a 6 i gael 9.

$$9$$

Ffactor

$$3^{2}$$