Whakaoti i te (sqrt{8}-2sqrt{25})-(sqrt{11/8}+sqrt{50}+2/3sqrt{12})

$$( \sqrt { 8 } - 2 \sqrt { 25 } ) - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Aromātai

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-10\approx -17.612701936$$

Ngā Upane Otinga

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}.

$$2\sqrt{2}-2\sqrt{25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tātaitia te pūtakerua o 25 kia tae ki 5.

$$2\sqrt{2}-2\times 5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-10-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Whakareatia te 1 ki te 8, ka 8.

$$2\sqrt{2}-10-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tāpirihia te 8 ki te 1, ka 9.

$$2\sqrt{2}-10-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{9}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{9}}{\sqrt{8}}.

$$2\sqrt{2}-10-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tātaitia te pūtakerua o 9 kia tae ki 3.

$$2\sqrt{2}-10-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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}.

$$2\sqrt{2}-10-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Whakangāwaritia te tauraro o \frac{3}{2\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Tauwehea te 50=5^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 2} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{2}. Tuhia te pūtakerua o te 5^{2}.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Pahekotia te \frac{3\sqrt{2}}{4} me 5\sqrt{2}, ka \frac{23}{4}\sqrt{2}.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

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}.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

Tuhia te \frac{2}{3}\times 2 hei hautanga kotahi.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

Hei kimi i te tauaro o \frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}, kimihia te tauaro o ia taurangi.

$$2\sqrt{2}-10-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

Pahekotia te 2\sqrt{2} me -\frac{23}{4}\sqrt{2}, ka -\frac{15}{4}\sqrt{2}.

$$-\frac{15}{4}\sqrt{2}-10-\frac{4}{3}\sqrt{3}$$

Tauwehe

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 120}{12} = -17.612701935657608$$