Whakaoti i te frac{sqrt{2}-4}{sqrt{5}+4}

$$\frac { \sqrt { 2 } - 4 } { \sqrt { 5 } + 4 }$$

Aromātai

$$\frac{4\sqrt{2}+4\sqrt{5}-\sqrt{10}-16}{11}\approx -0.414650136$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{2}-4}{\sqrt{5}+4} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}-4.

$$\frac{\left(\sqrt{2}-4\right)\left(\sqrt{5}-4\right)}{\left(\sqrt{5}+4\right)\left(\sqrt{5}-4\right)}$$

Whakaarohia te \left(\sqrt{5}+4\right)\left(\sqrt{5}-4\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}.

$$\frac{\left(\sqrt{2}-4\right)\left(\sqrt{5}-4\right)}{\left(\sqrt{5}\right)^{2}-4^{2}}$$

Pūrua \sqrt{5}. Pūrua 4.

$$\frac{\left(\sqrt{2}-4\right)\left(\sqrt{5}-4\right)}{5-16}$$

Tangohia te 16 i te 5, ka -11.

$$\frac{\left(\sqrt{2}-4\right)\left(\sqrt{5}-4\right)}{-11}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \sqrt{2}-4 ki ia tau o \sqrt{5}-4.

$$\frac{\sqrt{2}\sqrt{5}-4\sqrt{2}-4\sqrt{5}+16}{-11}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{10}-4\sqrt{2}-4\sqrt{5}+16}{-11}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-\sqrt{10}+4\sqrt{2}+4\sqrt{5}-16}{11}$$