Whakaoti i te sqrt{216}-2sqrt{54}-sqrt{160}+4sqrt{360}-2sqrt{50}

$$\sqrt{ 216 } -2 \sqrt{ 54 } - \sqrt{ 160 } +4 \sqrt{ 360 } -2 \sqrt{ 50 }$$

Aromātai

$$10\sqrt{2}\left(2\sqrt{5}-1\right)\approx 49.10341758$$

Ngā Upane Otinga

Tauwehea te 216=6^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 6} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{6}. Tuhia te pūtakerua o te 6^{2}.

$$6\sqrt{6}-2\sqrt{54}-\sqrt{160}+4\sqrt{360}-2\sqrt{50}$$

Tauwehea te 54=3^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 6} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{6}. Tuhia te pūtakerua o te 3^{2}.

$$6\sqrt{6}-2\times 3\sqrt{6}-\sqrt{160}+4\sqrt{360}-2\sqrt{50}$$

Whakareatia te -2 ki te 3, ka -6.

$$6\sqrt{6}-6\sqrt{6}-\sqrt{160}+4\sqrt{360}-2\sqrt{50}$$

Pahekotia te 6\sqrt{6} me -6\sqrt{6}, ka 0.

$$-\sqrt{160}+4\sqrt{360}-2\sqrt{50}$$

Tauwehea te 160=4^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 10} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{10}. Tuhia te pūtakerua o te 4^{2}.

$$-4\sqrt{10}+4\sqrt{360}-2\sqrt{50}$$

Tauwehea te 360=6^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 10} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{10}. Tuhia te pūtakerua o te 6^{2}.

$$-4\sqrt{10}+4\times 6\sqrt{10}-2\sqrt{50}$$

Whakareatia te 4 ki te 6, ka 24.

$$-4\sqrt{10}+24\sqrt{10}-2\sqrt{50}$$

Pahekotia te -4\sqrt{10} me 24\sqrt{10}, ka 20\sqrt{10}.

$$20\sqrt{10}-2\sqrt{50}$$

Tauwehea te 50=5^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 2} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{2}. Tuhia te pūtakerua o te 5^{2}.

$$20\sqrt{10}-2\times 5\sqrt{2}$$

Whakareatia te -2 ki te 5, ka -10.

$$20\sqrt{10}-10\sqrt{2}$$