Whakaoti i te sqrt{45}+3sqrt{20}+sqrt{80}+4sqrt{40}

$$\sqrt { 45 } + 3 \sqrt { 20 } + \sqrt { 80 } + 4 \sqrt { 40 }$$

Aromātai

$$8\sqrt{10}+13\sqrt{5}\approx 54.367104989$$

Ngā Upane Otinga

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}.

$$3\sqrt{5}+3\sqrt{20}+\sqrt{80}+4\sqrt{40}$$

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}.

$$3\sqrt{5}+3\times 2\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

Whakareatia te 3 ki te 2, ka 6.

$$3\sqrt{5}+6\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

Pahekotia te 3\sqrt{5} me 6\sqrt{5}, ka 9\sqrt{5}.

$$9\sqrt{5}+\sqrt{80}+4\sqrt{40}$$

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}.

$$9\sqrt{5}+4\sqrt{5}+4\sqrt{40}$$

Pahekotia te 9\sqrt{5} me 4\sqrt{5}, ka 13\sqrt{5}.

$$13\sqrt{5}+4\sqrt{40}$$

Tauwehea te 40=2^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 10} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{10}. Tuhia te pūtakerua o te 2^{2}.

$$13\sqrt{5}+4\times 2\sqrt{10}$$

Whakareatia te 4 ki te 2, ka 8.

$$13\sqrt{5}+8\sqrt{10}$$