Whakaoti i te sqrt{80}+5sqrt{1/2}-3sqrt{+1/5}sqrt{125}

$$\sqrt{ 80 } +5 \sqrt{ \frac{ 1 }{ 2 } } -3 \sqrt{ + \frac{ 1 }{ 5 } } \sqrt{ 125 }$$

Aromātai

$$\frac{5\sqrt{2}}{2}+4\sqrt{5}-15\approx -2.520194184$$

Ngā Hipanga Rongoā Poto

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}.

$$4\sqrt{5}+5\sqrt{\frac{1}{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$4\sqrt{5}+5\times \frac{\sqrt{1}}{\sqrt{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{5}+5\times \frac{1}{\sqrt{2}}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

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

Ko te pūrua o \sqrt{2} ko 2.

$$4\sqrt{5}+5\times \frac{\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Tuhia te 5\times \frac{\sqrt{2}}{2} hei hautanga kotahi.

$$4\sqrt{5}+\frac{5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4\sqrt{5} ki te \frac{2}{2}.

$$\frac{2\times 4\sqrt{5}}{2}+\frac{5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Tā te mea he rite te tauraro o \frac{2\times 4\sqrt{5}}{2} me \frac{5\sqrt{2}}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2\times 4\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

Mahia ngā whakarea i roto o 2\times 4\sqrt{5}+5\sqrt{2}.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{\frac{1}{5}}\sqrt{125}$$

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

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{125}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{1}{\sqrt{5}}\sqrt{125}$$

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

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{125}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{5}\sqrt{125}$$

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}.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\times \frac{\sqrt{5}}{5}\times 5\sqrt{5}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-15\times \frac{\sqrt{5}}{5}\sqrt{5}$$

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

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-3\sqrt{5}\sqrt{5}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 3\sqrt{5}\sqrt{5} ki te \frac{2}{2}.

$$\frac{8\sqrt{5}+5\sqrt{2}}{2}-\frac{2\times 3\sqrt{5}\sqrt{5}}{2}$$

Tā te mea he rite te tauraro o \frac{8\sqrt{5}+5\sqrt{2}}{2} me \frac{2\times 3\sqrt{5}\sqrt{5}}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{8\sqrt{5}+5\sqrt{2}-2\times 3\sqrt{5}\sqrt{5}}{2}$$

Mahia ngā whakarea i roto o 8\sqrt{5}+5\sqrt{2}-2\times 3\sqrt{5}\sqrt{5}.

$$\frac{8\sqrt{5}+5\sqrt{2}-30}{2}$$