Whakaoti i te sqrt{80}+5sqrt{1/5}-3sqrt{1/5}sqrt{125}

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 5 } } -3 \sqrt{ \frac{ 1 }{ 5 } } \sqrt{ 125 }$$

Aromātai

$$5\sqrt{5}-15\approx -3.819660113$$

Ngā Upane Otinga

Tauwehea te 80=4^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 5} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{5}. Tuhia te pūtakerua o te 4^{2}.

$$4\sqrt{5}+5\sqrt{\frac{1}{5}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{5}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{5}+5\times \frac{1}{\sqrt{5}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Ko te pūrua o \sqrt{5} ko 5.

$$4\sqrt{5}+5\times \frac{\sqrt{5}}{5}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Me whakakore te 5 me te 5.

$$4\sqrt{5}+\sqrt{5}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Pahekotia te 4\sqrt{5} me \sqrt{5}, ka 5\sqrt{5}.

$$5\sqrt{5}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$5\sqrt{5}-3\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{125}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$5\sqrt{5}-3\times \frac{1}{\sqrt{5}}\sqrt{125}$$

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

$$5\sqrt{5}-3\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{125}$$

Ko te pūrua o \sqrt{5} ko 5.

$$5\sqrt{5}-3\times \frac{\sqrt{5}}{5}\sqrt{125}$$

Tauwehea te 125=5^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 5} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{5}. Tuhia te pūtakerua o te 5^{2}.

$$5\sqrt{5}-3\times \frac{\sqrt{5}}{5}\times 5\sqrt{5}$$

Whakareatia te 3 ki te 5, ka 15.

$$5\sqrt{5}-15\times \frac{\sqrt{5}}{5}\sqrt{5}$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 15 me te 5.

$$5\sqrt{5}-3\sqrt{5}\sqrt{5}$$

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

$$5\sqrt{5}-3\times 5$$

Whakareatia te 3 ki te 5, ka 15.

$$5\sqrt{5}-15$$