Whakaoti i te sqrt{75}+3sqrt{18}-2sqrt{12}-2sqrt{50}

$$\sqrt { 75 } + 3 \sqrt { 18 } - 2 \sqrt { 12 } - 2 \sqrt { 50 }$$

Aromātai

$$\sqrt{3}-\sqrt{2}\approx 0.317837245$$

Ngā Upane Otinga

Tauwehea te 75=5^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 3} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{3}. Tuhia te pūtakerua o te 5^{2}.

$$5\sqrt{3}+3\sqrt{18}-2\sqrt{12}-2\sqrt{50}$$

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}.

$$5\sqrt{3}+3\times 3\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

Whakareatia te 3 ki te 3, ka 9.

$$5\sqrt{3}+9\sqrt{2}-2\sqrt{12}-2\sqrt{50}$$

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}.

$$5\sqrt{3}+9\sqrt{2}-2\times 2\sqrt{3}-2\sqrt{50}$$

Whakareatia te -2 ki te 2, ka -4.

$$5\sqrt{3}+9\sqrt{2}-4\sqrt{3}-2\sqrt{50}$$

Pahekotia te 5\sqrt{3} me -4\sqrt{3}, ka \sqrt{3}.

$$\sqrt{3}+9\sqrt{2}-2\sqrt{50}$$

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}.

$$\sqrt{3}+9\sqrt{2}-2\times 5\sqrt{2}$$

Whakareatia te -2 ki te 5, ka -10.

$$\sqrt{3}+9\sqrt{2}-10\sqrt{2}$$

Pahekotia te 9\sqrt{2} me -10\sqrt{2}, ka -\sqrt{2}.

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