Whakaoti i te frac{2sqrt{54}+8sqrt{6}}{6sqrt{12}-5sqrt{3}}

$$\frac { 2 \sqrt { 54 } + 8 \sqrt { 6 } } { 6 \sqrt { 12 } - 5 \sqrt { 3 } }$$

Aromātai

$$2\sqrt{2}\approx 2.828427125$$

Ngā Upane Otinga

Tauwehea te 54=3^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 6} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{6}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{2\times 3\sqrt{6}+8\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{6\sqrt{6}+8\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Pahekotia te 6\sqrt{6} me 8\sqrt{6}, ka 14\sqrt{6}.

$$\frac{14\sqrt{6}}{6\sqrt{12}-5\sqrt{3}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{14\sqrt{6}}{6\times 2\sqrt{3}-5\sqrt{3}}$$

Whakareatia te 6 ki te 2, ka 12.

$$\frac{14\sqrt{6}}{12\sqrt{3}-5\sqrt{3}}$$

Pahekotia te 12\sqrt{3} me -5\sqrt{3}, ka 7\sqrt{3}.

$$\frac{14\sqrt{6}}{7\sqrt{3}}$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

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

Me whakakore te 3 me te 3.

$$2\sqrt{2}$$