Whakaoti i te frac{sqrt{7}+sqrt{8}}{sqrt{10}}

$$\frac { \sqrt { 7 } + \sqrt { 8 } } { \sqrt { 10 } }$$

Aromātai

$$\frac{\sqrt{70}+4\sqrt{5}}{10}\approx 1.731087218$$

Ngā Upane Otinga

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}.

$$\frac{\sqrt{7}+2\sqrt{2}}{\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{7}+2\sqrt{2}}{\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{\left(\sqrt{7}+2\sqrt{2}\right)\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{\left(\sqrt{7}+2\sqrt{2}\right)\sqrt{10}}{10}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{7}+2\sqrt{2} ki te \sqrt{10}.

$$\frac{\sqrt{7}\sqrt{10}+2\sqrt{2}\sqrt{10}}{10}$$

Hei whakarea \sqrt{7} me \sqrt{10}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{70}+2\sqrt{2}\sqrt{10}}{10}$$

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}.

$$\frac{\sqrt{70}+2\sqrt{2}\sqrt{2}\sqrt{5}}{10}$$

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

$$\frac{\sqrt{70}+2\times 2\sqrt{5}}{10}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\sqrt{70}+4\sqrt{5}}{10}$$