Whakaoti i te frac{6sqrt{24}+sqrt{54}}{sqrt{50}}

$$\frac { 6 \sqrt { 24 } + \sqrt { 54 } } { \sqrt { 50 } }$$

Aromātai

$$3\sqrt{3}\approx 5.196152423$$

Ngā Upane Otinga

Tauwehea te 24=2^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 6} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{6}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{6\times 2\sqrt{6}+\sqrt{54}}{\sqrt{50}}$$

Whakareatia te 6 ki te 2, ka 12.

$$\frac{12\sqrt{6}+\sqrt{54}}{\sqrt{50}}$$

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}.

$$\frac{12\sqrt{6}+3\sqrt{6}}{\sqrt{50}}$$

Pahekotia te 12\sqrt{6} me 3\sqrt{6}, ka 15\sqrt{6}.

$$\frac{15\sqrt{6}}{\sqrt{50}}$$

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}.

$$\frac{15\sqrt{6}}{5\sqrt{2}}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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}.

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

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

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

Me whakakore te 2 me te 2.

$$3\sqrt{3}$$