Whakaoti i te 2sqrt{20}+2/3sqrt{45}-5/4sqrt{80}-sqrt{5}

$$2 \sqrt{ 20 } + \frac{ 2 }{ 3 } \sqrt{ 45 } - \frac{ 5 }{ 4 } \sqrt{ 80 } - \sqrt{ 5 }$$

Aromātai

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Ngā Upane Otinga

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}.

$$2\times 2\sqrt{5}+\frac{2}{3}\sqrt{45}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{5}+\frac{2}{3}\sqrt{45}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.

$$4\sqrt{5}+\frac{2}{3}\times 3\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Me whakakore te 3 me te 3.

$$4\sqrt{5}+2\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

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

$$6\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

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}.

$$6\sqrt{5}-\frac{5}{4}\times 4\sqrt{5}-\sqrt{5}$$

Me whakakore te 4 me te 4.

$$6\sqrt{5}-5\sqrt{5}-\sqrt{5}$$

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

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

Pahekotia te \sqrt{5} me -\sqrt{5}, ka 0.

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Tauwehe

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