Whakaoti i te (4sqrt{6}-4sqrt{1/2}+3sqrt{8})div2sqrt{2}=

$$( 4 \sqrt { 6 } - 4 \sqrt { \frac { 1 } { 2 } } + 3 \sqrt { 8 } ) \div 2 \sqrt { 2 } =$$

Aromātai

$$4\left(\sqrt{3}+1\right)\approx 10.92820323$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{1}}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{4\sqrt{6}-4\times \frac{1}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

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

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3\sqrt{8}}{2}\sqrt{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{2}+3\sqrt{8}}{2}\sqrt{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 4 me te 2.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\sqrt{8}}{2}\sqrt{2}$$

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}.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\times 2\sqrt{2}}{2}\sqrt{2}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{4\sqrt{6}-2\sqrt{2}+6\sqrt{2}}{2}\sqrt{2}$$

Pahekotia te -2\sqrt{2} me 6\sqrt{2}, ka 4\sqrt{2}.

$$\frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2}$$

Tuhia te \frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2} hei hautanga kotahi.

$$\frac{\left(4\sqrt{6}+4\sqrt{2}\right)\sqrt{2}}{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4\sqrt{6}+4\sqrt{2} ki te \sqrt{2}.

$$\frac{4\sqrt{6}\sqrt{2}+4\left(\sqrt{2}\right)^{2}}{2}$$

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

$$\frac{4\sqrt{2}\sqrt{3}\sqrt{2}+4\left(\sqrt{2}\right)^{2}}{2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{4\times 2\sqrt{3}+4\left(\sqrt{2}\right)^{2}}{2}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{8\sqrt{3}+4\left(\sqrt{2}\right)^{2}}{2}$$

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 4 ki te 2, ka 8.

$$\frac{8\sqrt{3}+8}{2}$$