Whakaoti i te sqrt{48}+5sqrt{12}-sqrt{147}+sqrt{75}

$$\sqrt{ 48 } +5 \sqrt{ 12 } - \sqrt{ 147 } + \sqrt{ 75 }$$

Aromātai

$$12\sqrt{3}\approx 20.784609691$$

Ngā Upane Otinga

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}.

$$4\sqrt{3}+5\sqrt{12}-\sqrt{147}+\sqrt{75}$$

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}.

$$4\sqrt{3}+5\times 2\sqrt{3}-\sqrt{147}+\sqrt{75}$$

Whakareatia te 5 ki te 2, ka 10.

$$4\sqrt{3}+10\sqrt{3}-\sqrt{147}+\sqrt{75}$$

Pahekotia te 4\sqrt{3} me 10\sqrt{3}, ka 14\sqrt{3}.

$$14\sqrt{3}-\sqrt{147}+\sqrt{75}$$

Tauwehea te 147=7^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 3} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{3}. Tuhia te pūtakerua o te 7^{2}.

$$14\sqrt{3}-7\sqrt{3}+\sqrt{75}$$

Pahekotia te 14\sqrt{3} me -7\sqrt{3}, ka 7\sqrt{3}.

$$7\sqrt{3}+\sqrt{75}$$

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}.

$$7\sqrt{3}+5\sqrt{3}$$

Pahekotia te 7\sqrt{3} me 5\sqrt{3}, ka 12\sqrt{3}.

$$12\sqrt{3}$$