Whakaoti i te sqrt{8}+1/2-2sqrt{1/2}

$$\sqrt { 8 } + \frac { 1 } { 2 } - 2 \sqrt { \frac { 1 } { 2 } }$$

Aromātai

$$\sqrt{2}+\frac{1}{2}\approx 1.914213562$$

Ngā Upane Otinga

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$2\sqrt{2}+\frac{1}{2}-2\sqrt{\frac{1}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{2}}.

$$2\sqrt{2}+\frac{1}{2}-2\times \frac{\sqrt{1}}{\sqrt{2}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$2\sqrt{2}+\frac{1}{2}-2\times \frac{1}{\sqrt{2}}$$

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

$$2\sqrt{2}+\frac{1}{2}-2\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\sqrt{2}+\frac{1}{2}-2\times \frac{\sqrt{2}}{2}$$

Me whakakore te 2 me te 2.

$$2\sqrt{2}+\frac{1}{2}-\sqrt{2}$$

Pahekotia te 2\sqrt{2} me -\sqrt{2}, ka \sqrt{2}.

$$\sqrt{2}+\frac{1}{2}$$

Tauwehe

$$\frac{2 \sqrt{2} + 1}{2} = 1.9142135623730951$$