Whakaoti i te 6sqrt{1/8}-sqrt{32}

$$6 \sqrt{ \frac{ 1 }{ 8 } } - \sqrt{ 32 }$$

Aromātai

$$-\frac{5\sqrt{2}}{2}\approx -3.535533906$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{8}}.

$$6\times \frac{\sqrt{1}}{\sqrt{8}}-\sqrt{32}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$6\times \frac{1}{\sqrt{8}}-\sqrt{32}$$

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}.

$$6\times \frac{1}{2\sqrt{2}}-\sqrt{32}$$

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

$$6\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{32}$$

Ko te pūrua o \sqrt{2} ko 2.

$$6\times \frac{\sqrt{2}}{2\times 2}-\sqrt{32}$$

Whakareatia te 2 ki te 2, ka 4.

$$6\times \frac{\sqrt{2}}{4}-\sqrt{32}$$

Tuhia te 6\times \frac{\sqrt{2}}{4} hei hautanga kotahi.

$$\frac{6\sqrt{2}}{4}-\sqrt{32}$$

Tauwehea te 32=4^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 2} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{2}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{6\sqrt{2}}{4}-4\sqrt{2}$$

Pahekotia te \frac{6\sqrt{2}}{4} me -4\sqrt{2}, ka -\frac{5}{2}\sqrt{2}.

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