Whakaoti i te frac{2*sqrt{343}+sqrt{125}}{sqrt{5}}

$$\frac { 2 \cdot \sqrt { 343 } + \sqrt { 125 } } { \sqrt { 5 } }$$

Aromātai

$$\frac{14\sqrt{35}}{5}+5\approx 21.565023393$$

Ngā Upane Otinga

Tauwehea te 343=7^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 7} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{7}. Tuhia te pūtakerua o te 7^{2}.

$$\frac{2\times 7\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

Whakareatia te 2 ki te 7, ka 14.

$$\frac{14\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

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}.

$$\frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{5}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 14\sqrt{7}+5\sqrt{5} ki te \sqrt{5}.

$$\frac{14\sqrt{7}\sqrt{5}+5\left(\sqrt{5}\right)^{2}}{5}$$

Hei whakarea \sqrt{7} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{14\sqrt{35}+5\left(\sqrt{5}\right)^{2}}{5}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{14\sqrt{35}+5\times 5}{5}$$

Whakareatia te 5 ki te 5, ka 25.

$$\frac{14\sqrt{35}+25}{5}$$