Whakaoti i te 5sqrt{1/5}*sqrt{20}-sqrt{40}divsqrt{8}

$$5 \sqrt{ \frac{ 1 }{ 5 } } \times \sqrt{ 20 } - \sqrt{ 40 } \div \sqrt{ 8 }$$

Aromātai

$$10-\sqrt{5}\approx 7.763932023$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{5}}.

$$5\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{20}-\frac{\sqrt{40}}{\sqrt{8}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$5\times \frac{1}{\sqrt{5}}\sqrt{20}-\frac{\sqrt{40}}{\sqrt{8}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{20}-\frac{\sqrt{40}}{\sqrt{8}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$5\times \frac{\sqrt{5}}{5}\sqrt{20}-\frac{\sqrt{40}}{\sqrt{8}}$$

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$5\times \frac{\sqrt{5}}{5}\times 2\sqrt{5}-\frac{\sqrt{40}}{\sqrt{8}}$$

Whakareatia te 5 ki te 2, ka 10.

$$10\times \frac{\sqrt{5}}{5}\sqrt{5}-\frac{\sqrt{40}}{\sqrt{8}}$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 10 me te 5.

$$2\sqrt{5}\sqrt{5}-\frac{\sqrt{40}}{\sqrt{8}}$$

Tuhia anō te whakawehe o ngā pūtake rua \frac{\sqrt{40}}{\sqrt{8}} hei pūtake rua o te whakawehenga \sqrt{\frac{40}{8}} ka mahi i te whakawehenga.

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

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

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

Whakareatia te 2 ki te 5, ka 10.

$$10-\sqrt{5}$$