Whakaoti i te 2sqrt{27}*sqrt{32}divsqrt{48}

$$2 \sqrt{ 27 } \times \sqrt{ 32 } \div \sqrt{ 48 }$$

Aromātai

$$6\sqrt{2}\approx 8.485281374$$

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}.

$$\frac{2\times 3\sqrt{3}\sqrt{32}}{\sqrt{48}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{6\sqrt{3}\sqrt{32}}{\sqrt{48}}$$

Tauwehea te 32=4^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 2} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{2}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{6\sqrt{3}\times 4\sqrt{2}}{\sqrt{48}}$$

Whakareatia te 6 ki te 4, ka 24.

$$\frac{24\sqrt{3}\sqrt{2}}{\sqrt{48}}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{24\sqrt{6}}{\sqrt{48}}$$

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}.

$$\frac{24\sqrt{6}}{4\sqrt{3}}$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

$$\frac{6\sqrt{6}}{\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{6\sqrt{6}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{6\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{6\sqrt{6}\sqrt{3}}{3}$$

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

$$\frac{6\sqrt{3}\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{6\times 3\sqrt{2}}{3}$$

Me whakakore te 3 me te 3.

$$6\sqrt{2}$$