Whakaoti i te (sqrt{18}+3sqrt{3}-sqrt{12})*2sqrt{3}

$$( \sqrt{ 18 } +3 \sqrt{ 3 } - \sqrt{ 12 } ) \times 2 \sqrt{ 3 }$$

Aromātai

$$6\sqrt{6}+6\approx 20.696938457$$

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}.

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

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}.

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

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

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

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

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

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

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

$$6\sqrt{6}+2\times 3$$

Whakareatia te 2 ki te 3, ka 6.

$$6\sqrt{6}+6$$