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2\times 3\sqrt{5}-\sqrt{50}+3\sqrt{75}
Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.
6\sqrt{5}-\sqrt{50}+3\sqrt{75}
Whakareatia te 2 ki te 3, ka 6.
6\sqrt{5}-5\sqrt{2}+3\sqrt{75}
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}.
6\sqrt{5}-5\sqrt{2}+3\times 5\sqrt{3}
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}.
6\sqrt{5}-5\sqrt{2}+15\sqrt{3}
Whakareatia te 3 ki te 5, ka 15.