Whakaoti i te sqrt{8}+sqrt{50}-sqrt{48}+sqrt{12}

$$\sqrt { 8 } + \sqrt { 50 } - \sqrt { 48 } + \sqrt { 12 }$$

Aromātai

$$7\sqrt{2}-2\sqrt{3}\approx 6.435393321$$

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}.

$$2\sqrt{2}+\sqrt{50}-\sqrt{48}+\sqrt{12}$$

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}.

$$2\sqrt{2}+5\sqrt{2}-\sqrt{48}+\sqrt{12}$$

Pahekotia te 2\sqrt{2} me 5\sqrt{2}, ka 7\sqrt{2}.

$$7\sqrt{2}-\sqrt{48}+\sqrt{12}$$

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}.

$$7\sqrt{2}-4\sqrt{3}+\sqrt{12}$$

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}.

$$7\sqrt{2}-4\sqrt{3}+2\sqrt{3}$$

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

$$7\sqrt{2}-2\sqrt{3}$$