Whakaoti i te 5sqrt{75}-2sqrt{108}+5sqrt{12}

$$5 \sqrt { 75 } - 2 \sqrt { 108 } + 5 \sqrt { 12 }$$

Aromātai

$$23\sqrt{3}\approx 39.837168574$$

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}.

$$5\times 5\sqrt{3}-2\sqrt{108}+5\sqrt{12}$$

Whakareatia te 5 ki te 5, ka 25.

$$25\sqrt{3}-2\sqrt{108}+5\sqrt{12}$$

Tauwehea te 108=6^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 3} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{3}. Tuhia te pūtakerua o te 6^{2}.

$$25\sqrt{3}-2\times 6\sqrt{3}+5\sqrt{12}$$

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

$$25\sqrt{3}-12\sqrt{3}+5\sqrt{12}$$

Pahekotia te 25\sqrt{3} me -12\sqrt{3}, ka 13\sqrt{3}.

$$13\sqrt{3}+5\sqrt{12}$$

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}.

$$13\sqrt{3}+5\times 2\sqrt{3}$$

Whakareatia te 5 ki te 2, ka 10.

$$13\sqrt{3}+10\sqrt{3}$$

Pahekotia te 13\sqrt{3} me 10\sqrt{3}, ka 23\sqrt{3}.

$$23\sqrt{3}$$