Whakaoti i te (2sqrt{8}-3sqrt{3}+5sqrt{32})-(3sqrt{27}-6sqrt{24})

$$( 2 \sqrt { 8 } - 3 \sqrt { 3 } + 5 \sqrt { 32 } ) - ( 3 \sqrt { 27 } - 6 \sqrt { 24 } )$$

Aromātai

$$12\left(\sqrt{6}+2\sqrt{2}-\sqrt{3}\right)\approx 42.55039272$$

Ngā Upane Otinga

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$2\times 2\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Tauwehea te 32=4^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 2} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{2}. Tuhia te pūtakerua o te 4^{2}.

$$4\sqrt{2}-3\sqrt{3}+5\times 4\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Whakareatia te 5 ki te 4, ka 20.

$$4\sqrt{2}-3\sqrt{3}+20\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Pahekotia te 4\sqrt{2} me 20\sqrt{2}, ka 24\sqrt{2}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

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}.

$$24\sqrt{2}-3\sqrt{3}-\left(3\times 3\sqrt{3}-6\sqrt{24}\right)$$

Whakareatia te 3 ki te 3, ka 9.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\sqrt{24}\right)$$

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}.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\times 2\sqrt{6}\right)$$

Whakareatia te -6 ki te 2, ka -12.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-12\sqrt{6}\right)$$

Hei kimi i te tauaro o 9\sqrt{3}-12\sqrt{6}, kimihia te tauaro o ia taurangi.

$$24\sqrt{2}-3\sqrt{3}-9\sqrt{3}-\left(-12\sqrt{6}\right)$$

Pahekotia te -3\sqrt{3} me -9\sqrt{3}, ka -12\sqrt{3}.

$$24\sqrt{2}-12\sqrt{3}-\left(-12\sqrt{6}\right)$$

Ko te tauaro o -12\sqrt{6} ko 12\sqrt{6}.

$$24\sqrt{2}-12\sqrt{3}+12\sqrt{6}$$