Whakaoti i te 3*sqrt{18}+1/5sqrt{50}-4*sqrt{1/2}

$$3 \times \sqrt { 18 } + \frac { 1 } { 5 } \sqrt { 50 } - 4 \times \sqrt { \frac { 1 } { 2 } }$$

Aromātai

$$8\sqrt{2}\approx 11.313708499$$

Ngā Upane Otinga

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}.

$$3\times 3\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

Whakareatia te 3 ki te 3, ka 9.

$$9\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

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}.

$$9\sqrt{2}+\frac{1}{5}\times 5\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Me whakakore te 5 me te 5.

$$9\sqrt{2}+\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Pahekotia te 9\sqrt{2} me \sqrt{2}, ka 10\sqrt{2}.

$$10\sqrt{2}-4\sqrt{\frac{1}{2}}$$

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

$$10\sqrt{2}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$10\sqrt{2}-4\times \frac{1}{\sqrt{2}}$$

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

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{2}$$

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

$$10\sqrt{2}-2\sqrt{2}$$

Pahekotia te 10\sqrt{2} me -2\sqrt{2}, ka 8\sqrt{2}.

$$8\sqrt{2}$$