Datrys 1/sqrt{2008-sqrt{200}}

$$\frac { 1 } { \sqrt { 2008 } - \sqrt { 200 } }$$

Enrhifo

$$\frac{\sqrt{502}+5\sqrt{2}}{904}\approx 0.032606664$$

Camau Ateb

Ffactora 2008=2^{2}\times 502. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 502} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{502}. Cymryd isradd 2^{2}.

$$\frac{1}{2\sqrt{502}-\sqrt{200}}$$

Ffactora 200=10^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{10^{2}\times 2} fel lluoswm ail israddau \sqrt{10^{2}}\sqrt{2}. Cymryd isradd 10^{2}.

$$\frac{1}{2\sqrt{502}-10\sqrt{2}}$$

Mae'n rhesymoli enwadur \frac{1}{2\sqrt{502}-10\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â 2\sqrt{502}+10\sqrt{2}.

$$\frac{2\sqrt{502}+10\sqrt{2}}{\left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\sqrt{2}\right)}$$

Ystyriwch \left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\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}.

$$\frac{2\sqrt{502}+10\sqrt{2}}{\left(2\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

Ehangu \left(2\sqrt{502}\right)^{2}.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2^{2}\left(\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

$$\frac{2\sqrt{502}+10\sqrt{2}}{4\left(\sqrt{502}\right)^{2}-\left(-10\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{502} yw 502.

$$\frac{2\sqrt{502}+10\sqrt{2}}{4\times 502-\left(-10\sqrt{2}\right)^{2}}$$

Lluosi 4 a 502 i gael 2008.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-\left(-10\sqrt{2}\right)^{2}}$$

Ehangu \left(-10\sqrt{2}\right)^{2}.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-\left(-10\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Cyfrifo -10 i bŵer 2 a chael 100.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-100\left(\sqrt{2}\right)^{2}}$$

Sgwâr \sqrt{2} yw 2.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-100\times 2}$$

Lluosi 100 a 2 i gael 200.

$$\frac{2\sqrt{502}+10\sqrt{2}}{2008-200}$$

Tynnu 200 o 2008 i gael 1808.

$$\frac{2\sqrt{502}+10\sqrt{2}}{1808}$$