Whakaoti i te (3)3sqrt{48}-9sqrt{1/3}+3sqrt{12}

$$( 3 ) 3 \sqrt { 48 } - 9 \sqrt { \frac { 1 } { 3 } } + 3 \sqrt { 12 }$$

Aromātai

$$39\sqrt{3}\approx 67.549981495$$

Ngā Upane Otinga

Whakareatia te 3 ki te 3, ka 9.

$$9\sqrt{48}-9\sqrt{\frac{1}{3}}+3\sqrt{12}$$

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$9\times 4\sqrt{3}-9\sqrt{\frac{1}{3}}+3\sqrt{12}$$

Whakareatia te 9 ki te 4, ka 36.

$$36\sqrt{3}-9\sqrt{\frac{1}{3}}+3\sqrt{12}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$36\sqrt{3}-9\times \frac{\sqrt{1}}{\sqrt{3}}+3\sqrt{12}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$36\sqrt{3}-9\times \frac{1}{\sqrt{3}}+3\sqrt{12}$$

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

$$36\sqrt{3}-9\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+3\sqrt{12}$$

Ko te pūrua o \sqrt{3} ko 3.

$$36\sqrt{3}-9\times \frac{\sqrt{3}}{3}+3\sqrt{12}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 9 me te 3.

$$36\sqrt{3}-3\sqrt{3}+3\sqrt{12}$$

Pahekotia te 36\sqrt{3} me -3\sqrt{3}, ka 33\sqrt{3}.

$$33\sqrt{3}+3\sqrt{12}$$

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}.

$$33\sqrt{3}+3\times 2\sqrt{3}$$

Whakareatia te 3 ki te 2, ka 6.

$$33\sqrt{3}+6\sqrt{3}$$

Pahekotia te 33\sqrt{3} me 6\sqrt{3}, ka 39\sqrt{3}.

$$39\sqrt{3}$$