Whakaoti i te sqrt{15}(2sqrt{5}+sqrt{3})-2sqrt{75}=

$$\sqrt { 15 } ( 2 \sqrt { 5 } + \sqrt { 3 } ) - 2 \sqrt { 75 } =$$

Aromātai

$$3\sqrt{5}\approx 6.708203932$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{15} ki te 2\sqrt{5}+\sqrt{3}.

$$2\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Tauwehea te 15=5\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5\times 3} hei hua o ngā pūtake rua \sqrt{5}\sqrt{3}.

$$2\sqrt{5}\sqrt{3}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

$$2\times 5\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Whakareatia te 2 ki te 5, ka 10.

$$10\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Tauwehea te 15=3\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3\times 5} hei hua o ngā pūtake rua \sqrt{3}\sqrt{5}.

$$10\sqrt{3}+\sqrt{3}\sqrt{5}\sqrt{3}-2\sqrt{75}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$10\sqrt{3}+3\sqrt{5}-2\sqrt{75}$$

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}.

$$10\sqrt{3}+3\sqrt{5}-2\times 5\sqrt{3}$$

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

$$10\sqrt{3}+3\sqrt{5}-10\sqrt{3}$$

Pahekotia te 10\sqrt{3} me -10\sqrt{3}, ka 0.

$$3\sqrt{5}$$