Whakaoti i te sqrt{32}-sqrt{75}-sqrt{05}-2sqrt{1/3}=

$$\sqrt { 32 } - \sqrt { 75 } - \sqrt { 05 } - 2 \sqrt { \frac { 1 } { 3 } } =$$

Aromātai

$$-\frac{17\sqrt{3}}{3}+4\sqrt{2}\approx -4.158100327$$

Ngā Hipanga Rongoā Poto

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}.

$$4\sqrt{2}-\sqrt{75}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

Tauwehea te 75=5^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 3} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{3}. Tuhia te pūtakerua o te 5^{2}.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

Whakareatia te 0 ki te 5, ka 0.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0}-2\sqrt{\frac{1}{3}}$$

Tātaitia te pūtakerua o 0 kia tae ki 0.

$$4\sqrt{2}-5\sqrt{3}-0-2\sqrt{\frac{1}{3}}$$

Whakareatia te -1 ki te 0, ka 0.

$$4\sqrt{2}-5\sqrt{3}+0-2\sqrt{\frac{1}{3}}$$

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

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{1}{\sqrt{3}}$$

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

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{3}$$

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

$$4\sqrt{2}-5\sqrt{3}+0+\frac{-2\sqrt{3}}{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4\sqrt{2}-5\sqrt{3}+0 ki te \frac{3}{3}.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3}+\frac{-2\sqrt{3}}{3}$$

Tā te mea he rite te tauraro o \frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3} me \frac{-2\sqrt{3}}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3}}{3}$$

Mahia ngā whakarea i roto o 3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3}.

$$\frac{12\sqrt{2}-15\sqrt{3}-2\sqrt{3}}{3}$$

Mahia ngā tātaitai i roto o 12\sqrt{2}-15\sqrt{3}-2\sqrt{3}.

$$\frac{12\sqrt{2}-17\sqrt{3}}{3}$$