Whakaoti i te sqrt{2/5}*sqrt{50}-sqrt{45}

$$\sqrt { \frac { 2 } { 5 } } \times \sqrt { 50 } - \sqrt { 45 }$$

Aromātai

$$-\sqrt{5}\approx -2.236067977$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{5}}.

$$\frac{\sqrt{2}}{\sqrt{5}}\sqrt{50}-\sqrt{45}$$

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{50}-\sqrt{45}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\sqrt{2}\sqrt{5}}{5}\sqrt{50}-\sqrt{45}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{10}}{5}\sqrt{50}-\sqrt{45}$$

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}.

$$\frac{\sqrt{10}}{5}\times 5\sqrt{2}-\sqrt{45}$$

Me whakakore te 5 me te 5.

$$\sqrt{10}\sqrt{2}-\sqrt{45}$$

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

$$\sqrt{2}\sqrt{5}\sqrt{2}-\sqrt{45}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$2\sqrt{5}-\sqrt{45}$$

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}.

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

Pahekotia te 2\sqrt{5} me -3\sqrt{5}, ka -\sqrt{5}.

$$-\sqrt{5}$$