Whakaoti i te 1/3sqrt{27}+3/4sqrt{48}+1/2sqrt{12}

$$\frac{ 1 }{ 3 } \sqrt{ 27 } + \frac{ 3 }{ 4 } \sqrt{ 48 } + \frac{ 1 }{ 2 } \sqrt{ 12 }$$

Aromātai

$$5\sqrt{3}\approx 8.660254038$$

Ngā Upane Otinga

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{1}{3}\times 3\sqrt{3}+\frac{3}{4}\sqrt{48}+\frac{1}{2}\sqrt{12}$$

Me whakakore te 3 me te 3.

$$\sqrt{3}+\frac{3}{4}\sqrt{48}+\frac{1}{2}\sqrt{12}$$

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}.

$$\sqrt{3}+\frac{3}{4}\times 4\sqrt{3}+\frac{1}{2}\sqrt{12}$$

Me whakakore te 4 me te 4.

$$\sqrt{3}+3\sqrt{3}+\frac{1}{2}\sqrt{12}$$

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

$$4\sqrt{3}+\frac{1}{2}\sqrt{12}$$

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}.

$$4\sqrt{3}+\frac{1}{2}\times 2\sqrt{3}$$

Me whakakore te 2 me te 2.

$$4\sqrt{3}+\sqrt{3}$$

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

$$5\sqrt{3}$$