Whakaoti i te sqrt{12}(3sqrt{50}-sqrt{162})-sqrt{18}(sqrt{432}-sqrt{192})

$$\sqrt { 12 } ( 3 \sqrt { 50 } - \sqrt { 162 } ) - \sqrt { 18 } ( \sqrt { 432 } - \sqrt { 192 } )$$

Aromātai

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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}.

$$2\sqrt{3}\left(3\sqrt{50}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Tauwehea te 50=5^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 2} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{2}. Tuhia te pūtakerua o te 5^{2}.

$$2\sqrt{3}\left(3\times 5\sqrt{2}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Whakareatia te 3 ki te 5, ka 15.

$$2\sqrt{3}\left(15\sqrt{2}-\sqrt{162}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Tauwehea te 162=9^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{9^{2}\times 2} hei hua o ngā pūtake rua \sqrt{9^{2}}\sqrt{2}. Tuhia te pūtakerua o te 9^{2}.

$$2\sqrt{3}\left(15\sqrt{2}-9\sqrt{2}\right)-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Pahekotia te 15\sqrt{2} me -9\sqrt{2}, ka 6\sqrt{2}.

$$2\sqrt{3}\times 6\sqrt{2}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

Whakareatia te 2 ki te 6, ka 12.

$$12\sqrt{3}\sqrt{2}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

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

$$12\sqrt{6}-\sqrt{18}\left(\sqrt{432}-\sqrt{192}\right)$$

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}.

$$12\sqrt{6}-3\sqrt{2}\left(\sqrt{432}-\sqrt{192}\right)$$

Tauwehea te 432=12^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{12^{2}\times 3} hei hua o ngā pūtake rua \sqrt{12^{2}}\sqrt{3}. Tuhia te pūtakerua o te 12^{2}.

$$12\sqrt{6}-3\sqrt{2}\left(12\sqrt{3}-\sqrt{192}\right)$$

Tauwehea te 192=8^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{8^{2}\times 3} hei hua o ngā pūtake rua \sqrt{8^{2}}\sqrt{3}. Tuhia te pūtakerua o te 8^{2}.

$$12\sqrt{6}-3\sqrt{2}\left(12\sqrt{3}-8\sqrt{3}\right)$$

Pahekotia te 12\sqrt{3} me -8\sqrt{3}, ka 4\sqrt{3}.

$$12\sqrt{6}-3\sqrt{2}\times 4\sqrt{3}$$

Whakareatia te 3 ki te 4, ka 12.

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

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

$$12\sqrt{6}-12\sqrt{6}$$

Pahekotia te 12\sqrt{6} me -12\sqrt{6}, ka 0.

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Tauwehe

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