Whakaoti i te 2sqrt{48}-18sqrt{1/3}+3sqrt{18}-8sqrt{1/8}

$$2 \sqrt{ 48 } -18 \sqrt{ \frac{ 1 }{ 3 } } +3 \sqrt{ 18 } -8 \sqrt{ \frac{ 1 }{ 8 } }$$

Aromātai

$$\sqrt{2}\left(\sqrt{6}+7\right)\approx 13.363596552$$

Ngā Upane Otinga

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}.

$$2\times 4\sqrt{3}-18\sqrt{\frac{1}{3}}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Whakareatia te 2 ki te 4, ka 8.

$$8\sqrt{3}-18\sqrt{\frac{1}{3}}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$8\sqrt{3}-18\times \frac{\sqrt{1}}{\sqrt{3}}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$8\sqrt{3}-18\times \frac{1}{\sqrt{3}}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$8\sqrt{3}-18\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$8\sqrt{3}-18\times \frac{\sqrt{3}}{3}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 18 me te 3.

$$8\sqrt{3}-6\sqrt{3}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Pahekotia te 8\sqrt{3} me -6\sqrt{3}, ka 2\sqrt{3}.

$$2\sqrt{3}+3\sqrt{18}-8\sqrt{\frac{1}{8}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$2\sqrt{3}+3\times 3\sqrt{2}-8\sqrt{\frac{1}{8}}$$

Whakareatia te 3 ki te 3, ka 9.

$$2\sqrt{3}+9\sqrt{2}-8\sqrt{\frac{1}{8}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{8}}.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{\sqrt{1}}{\sqrt{8}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{1}{\sqrt{8}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{1}{2\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{1}{2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{\sqrt{2}}{2\times 2}$$

Whakareatia te 2 ki te 2, ka 4.

$$2\sqrt{3}+9\sqrt{2}-8\times \frac{\sqrt{2}}{4}$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 8 me te 4.

$$2\sqrt{3}+9\sqrt{2}-2\sqrt{2}$$

Pahekotia te 9\sqrt{2} me -2\sqrt{2}, ka 7\sqrt{2}.

$$2\sqrt{3}+7\sqrt{2}$$