Whakaoti i te sqrt{80}-2sqrt{252}+3sqrt{405}-3sqrt{500}

$$\sqrt { 80 } - 2 \sqrt { 252 } + 3 \sqrt { 405 } - 3 \sqrt { 500 }$$

Aromātai

$$\sqrt{5}-12\sqrt{7}\approx -29.512947755$$

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}.

$$4\sqrt{5}-2\sqrt{252}+3\sqrt{405}-3\sqrt{500}$$

Tauwehea te 252=6^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 7} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{7}. Tuhia te pūtakerua o te 6^{2}.

$$4\sqrt{5}-2\times 6\sqrt{7}+3\sqrt{405}-3\sqrt{500}$$

Whakareatia te -2 ki te 6, ka -12.

$$4\sqrt{5}-12\sqrt{7}+3\sqrt{405}-3\sqrt{500}$$

Tauwehea te 405=9^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{9^{2}\times 5} hei hua o ngā pūtake rua \sqrt{9^{2}}\sqrt{5}. Tuhia te pūtakerua o te 9^{2}.

$$4\sqrt{5}-12\sqrt{7}+3\times 9\sqrt{5}-3\sqrt{500}$$

Whakareatia te 3 ki te 9, ka 27.

$$4\sqrt{5}-12\sqrt{7}+27\sqrt{5}-3\sqrt{500}$$

Pahekotia te 4\sqrt{5} me 27\sqrt{5}, ka 31\sqrt{5}.

$$31\sqrt{5}-12\sqrt{7}-3\sqrt{500}$$

Tauwehea te 500=10^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{10^{2}\times 5} hei hua o ngā pūtake rua \sqrt{10^{2}}\sqrt{5}. Tuhia te pūtakerua o te 10^{2}.

$$31\sqrt{5}-12\sqrt{7}-3\times 10\sqrt{5}$$

Whakareatia te -3 ki te 10, ka -30.

$$31\sqrt{5}-12\sqrt{7}-30\sqrt{5}$$

Pahekotia te 31\sqrt{5} me -30\sqrt{5}, ka \sqrt{5}.

$$\sqrt{5}-12\sqrt{7}$$