Whakaoti i te (sqrt{18}-sqrt{12}+sqrt{2})*2sqrt{6}

$$( \sqrt { 18 } - \sqrt { 12 } + \sqrt { 2 } ) \times 2 \sqrt { 6 }$$

Aromātai

$$16\sqrt{3}-12\sqrt{2}\approx 10.742250173$$

Ngā Upane Otinga

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$2\left(3\sqrt{2}-\sqrt{12}+\sqrt{2}\right)\sqrt{6}$$

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}.

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

Pahekotia te 3\sqrt{2} me \sqrt{2}, ka 4\sqrt{2}.

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

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

$$\left(8\sqrt{2}-4\sqrt{3}\right)\sqrt{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8\sqrt{2}-4\sqrt{3} ki te \sqrt{6}.

$$8\sqrt{2}\sqrt{6}-4\sqrt{3}\sqrt{6}$$

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}.

$$8\sqrt{2}\sqrt{2}\sqrt{3}-4\sqrt{3}\sqrt{6}$$

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

$$8\times 2\sqrt{3}-4\sqrt{3}\sqrt{6}$$

Whakareatia te 8 ki te 2, ka 16.

$$16\sqrt{3}-4\sqrt{3}\sqrt{6}$$

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}.

$$16\sqrt{3}-4\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$16\sqrt{3}-4\times 3\sqrt{2}$$

Whakareatia te -4 ki te 3, ka -12.

$$16\sqrt{3}-12\sqrt{2}$$