Whakaoti i te (sqrt{45}+sqrt{18})-(sqrt{8}-sqrt{125})

$$( \sqrt{ 45 } + \sqrt{ 18 } )-( \sqrt{ 8 } - \sqrt{ 125 } )$$

Aromātai

$$\sqrt{2}+8\sqrt{5}\approx 19.302757382$$

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}.

$$3\sqrt{5}+\sqrt{18}-\left(\sqrt{8}-\sqrt{125}\right)$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

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

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$3\sqrt{5}+3\sqrt{2}-\left(2\sqrt{2}-\sqrt{125}\right)$$

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}.

$$3\sqrt{5}+3\sqrt{2}-\left(2\sqrt{2}-5\sqrt{5}\right)$$

Hei kimi i te tauaro o 2\sqrt{2}-5\sqrt{5}, kimihia te tauaro o ia taurangi.

$$3\sqrt{5}+3\sqrt{2}-2\sqrt{2}-\left(-5\sqrt{5}\right)$$

Pahekotia te 3\sqrt{2} me -2\sqrt{2}, ka \sqrt{2}.

$$3\sqrt{5}+\sqrt{2}-\left(-5\sqrt{5}\right)$$

Ko te tauaro o -5\sqrt{5} ko 5\sqrt{5}.

$$3\sqrt{5}+\sqrt{2}+5\sqrt{5}$$

Pahekotia te 3\sqrt{5} me 5\sqrt{5}, ka 8\sqrt{5}.

$$8\sqrt{5}+\sqrt{2}$$