Réitigh 1/sqrt{2008-sqrt{200}}

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

Luacháil

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

Céimeanna Réitigh

Fachtóirigh 2008=2^{2}\times 502. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 502} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{502}. Tóg fréamh chearnach 2^{2}.

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

Fachtóirigh 200=10^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{10^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{10^{2}}\sqrt{2}. Tóg fréamh chearnach 10^{2}.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 2\sqrt{502}+10\sqrt{2} chun ainmneoir \frac{1}{2\sqrt{502}-10\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\sqrt{2}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Fairsingigh \left(2\sqrt{502}\right)^{2}

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

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 502 uimhir chearnach \sqrt{502}.

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

Méadaigh 4 agus 502 chun 2008 a fháil.

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

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

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

Ríomh cumhacht -10 de 2 agus faigh 100.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Méadaigh 100 agus 2 chun 200 a fháil.

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

Dealaigh 200 ó 2008 chun 1808 a fháil.

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