Whakaoti i te 2sqrt{12}-18sqrt{1/27}+3sqrt{148}

$$2 \sqrt { 12 } - 18 \sqrt { \frac { 1 } { 27 } } + 3 \sqrt { 148 }$$

Aromātai

$$2\sqrt{3}\left(\sqrt{111}+1\right)\approx 39.960676797$$

Ngā Upane Otinga

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}.

$$2\times 2\sqrt{3}-18\sqrt{\frac{1}{27}}+3\sqrt{148}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{3}-18\sqrt{\frac{1}{27}}+3\sqrt{148}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{27}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{27}}.

$$4\sqrt{3}-18\times \frac{\sqrt{1}}{\sqrt{27}}+3\sqrt{148}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{3}-18\times \frac{1}{\sqrt{27}}+3\sqrt{148}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$4\sqrt{3}-18\times \frac{1}{3\sqrt{3}}+3\sqrt{148}$$

Whakangāwaritia te tauraro o \frac{1}{3\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$4\sqrt{3}-18\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}+3\sqrt{148}$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\sqrt{3}-18\times \frac{\sqrt{3}}{3\times 3}+3\sqrt{148}$$

Whakareatia te 3 ki te 3, ka 9.

$$4\sqrt{3}-18\times \frac{\sqrt{3}}{9}+3\sqrt{148}$$

Whakakorea atu te tauwehe pūnoa nui rawa 9 i roto i te 18 me te 9.

$$4\sqrt{3}-2\sqrt{3}+3\sqrt{148}$$

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

$$2\sqrt{3}+3\sqrt{148}$$

Tauwehea te 148=2^{2}\times 37. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 37} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{37}. Tuhia te pūtakerua o te 2^{2}.

$$2\sqrt{3}+3\times 2\sqrt{37}$$

Whakareatia te 3 ki te 2, ka 6.

$$2\sqrt{3}+6\sqrt{37}$$