Whakaoti i te (frac{sqrt{2}}{sqrt{2}-18})^2

$$( \frac { \sqrt { 2 } } { \sqrt { 2 } - 18 } ) ^ { 2 }$$

Aromātai

$$\frac{18\sqrt{2}+163}{25921}\approx 0.007270393$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{2}-18} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}+18.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right)}\right)^{2}$$

Whakaarohia te \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\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}.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}\right)^{2}-18^{2}}\right)^{2}$$

Pūrua \sqrt{2}. Pūrua 18.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{2-324}\right)^{2}$$

Tangohia te 324 i te 2, ka -322.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322}\right)^{2}$$

Kia whakarewa i te \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}}{\left(-322\right)^{2}}$$

Whakarohaina te \left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}.

$$\frac{\left(\sqrt{2}\right)^{2}\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{2}+18\right)^{2}.

$$\frac{2\left(\left(\sqrt{2}\right)^{2}+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(2+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Tāpirihia te 2 ki te 324, ka 326.

$$\frac{2\left(326+36\sqrt{2}\right)}{\left(-322\right)^{2}}$$

Tātaihia te -322 mā te pū o 2, kia riro ko 103684.

$$\frac{2\left(326+36\sqrt{2}\right)}{103684}$$

Whakawehea te 2\left(326+36\sqrt{2}\right) ki te 103684, kia riro ko \frac{1}{51842}\left(326+36\sqrt{2}\right).

$$\frac{1}{51842}\left(326+36\sqrt{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{51842} ki te 326+36\sqrt{2}.

$$\frac{163}{25921}+\frac{18}{25921}\sqrt{2}$$

Whakaroha

$$\frac{18 \sqrt{2} + 163}{25921} = 0.007270392505023561$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{2}-18} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}+18.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right)}\right)^{2}$$

Whakaarohia te \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\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}.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}\right)^{2}-18^{2}}\right)^{2}$$

Pūrua \sqrt{2}. Pūrua 18.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{2-324}\right)^{2}$$

Tangohia te 324 i te 2, ka -322.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322}\right)^{2}$$

Kia whakarewa i te \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}}{\left(-322\right)^{2}}$$

Whakarohaina te \left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}.

$$\frac{\left(\sqrt{2}\right)^{2}\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{2}+18\right)^{2}.

$$\frac{2\left(\left(\sqrt{2}\right)^{2}+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(2+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Tāpirihia te 2 ki te 324, ka 326.

$$\frac{2\left(326+36\sqrt{2}\right)}{\left(-322\right)^{2}}$$

Tātaihia te -322 mā te pū o 2, kia riro ko 103684.

$$\frac{2\left(326+36\sqrt{2}\right)}{103684}$$

Whakawehea te 2\left(326+36\sqrt{2}\right) ki te 103684, kia riro ko \frac{1}{51842}\left(326+36\sqrt{2}\right).

$$\frac{1}{51842}\left(326+36\sqrt{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{51842} ki te 326+36\sqrt{2}.

$$\frac{163}{25921}+\frac{18}{25921}\sqrt{2}$$