Whakaoti i te 1/sqrt{2008-sqrt{200}}

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

Aromātai

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

Ngā Upane Otinga

Tauwehea te 2008=2^{2}\times 502. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 502} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{502}. Tuhia te pūtakerua o te 2^{2}.

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

Tauwehea te 200=10^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{10^{2}\times 2} hei hua o ngā pūtake rua \sqrt{10^{2}}\sqrt{2}. Tuhia te pūtakerua o te 10^{2}.

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

Whakangāwaritia te tauraro o \frac{1}{2\sqrt{502}-10\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 2\sqrt{502}+10\sqrt{2}.

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

Whakaarohia te \left(2\sqrt{502}-10\sqrt{2}\right)\left(2\sqrt{502}+10\sqrt{2}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{502} ko 502.

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

Whakareatia te 4 ki te 502, ka 2008.

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

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

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

Tātaihia te -10 mā te pū o 2, kia riro ko 100.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 100 ki te 2, ka 200.

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

Tangohia te 200 i te 2008, ka 1808.

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