Whakaoti i te frac{sqrt{96}+3sqrt{3}}{sqrt{2}}=

$$\frac { \sqrt { 96 } + 3 \sqrt { 3 } } { \sqrt { 2 } } =$$

Aromātai

$$\frac{\sqrt{3}\left(3\sqrt{2}+8\right)}{2}\approx 10.602437844$$

Ngā Upane Otinga

Tauwehea te 96=4^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 6} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{6}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{4\sqrt{6}+3\sqrt{3}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{4\sqrt{6}+3\sqrt{3}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\left(4\sqrt{6}+3\sqrt{3}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\left(4\sqrt{6}+3\sqrt{3}\right)\sqrt{2}}{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4\sqrt{6}+3\sqrt{3} ki te \sqrt{2}.

$$\frac{4\sqrt{6}\sqrt{2}+3\sqrt{3}\sqrt{2}}{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$\frac{4\sqrt{2}\sqrt{3}\sqrt{2}+3\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{4\times 2\sqrt{3}+3\sqrt{3}\sqrt{2}}{2}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{8\sqrt{3}+3\sqrt{3}\sqrt{2}}{2}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{8\sqrt{3}+3\sqrt{6}}{2}$$