Whakaoti i te (sqrt{32}+sqrt{05}-2sqrt{1/3})-(sqrt{1/8}-sqrt{75})

$$( \sqrt { 32 } + \sqrt { 05 } - 2 \sqrt { \frac { 1 } { 3 } } ) - ( \sqrt { \frac { 1 } { 8 } } - \sqrt { 75 } )$$

Aromātai

$$\frac{13\sqrt{3}}{3}+\frac{15\sqrt{2}}{4}\approx 12.808854358$$

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}.

$$4\sqrt{2}+\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

Whakareatia te 0 ki te 5, ka 0.

$$4\sqrt{2}+\sqrt{0}-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

Tātaitia te pūtakerua o 0 kia tae ki 0.

$$4\sqrt{2}+0-2\sqrt{\frac{1}{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{2}+0-2\times \frac{1}{\sqrt{3}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\sqrt{2}+0-2\times \frac{\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$4\sqrt{2}+0+\frac{-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{3\left(4\sqrt{2}+0\right)}{3}+\frac{-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{3\left(4\sqrt{2}+0\right)-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{1}}{\sqrt{8}}-\sqrt{75}\right)$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{1}{\sqrt{8}}-\sqrt{75}\right)$$

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}.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{1}{2\sqrt{2}}-\sqrt{75}\right)$$

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{75}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{2\times 2}-\sqrt{75}\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\left(\frac{\sqrt{2}}{4}-\sqrt{75}\right)$$

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}.

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

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

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

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

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

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

$$\frac{12\sqrt{2}-2\sqrt{3}}{3}-\frac{\sqrt{2}-20\sqrt{3}}{4}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 3 me 4 ko 12. Whakareatia \frac{12\sqrt{2}-2\sqrt{3}}{3} ki te \frac{4}{4}. Whakareatia \frac{\sqrt{2}-20\sqrt{3}}{4} ki te \frac{3}{3}.

$$\frac{4\left(12\sqrt{2}-2\sqrt{3}\right)}{12}-\frac{3\left(\sqrt{2}-20\sqrt{3}\right)}{12}$$

Tā te mea he rite te tauraro o \frac{4\left(12\sqrt{2}-2\sqrt{3}\right)}{12} me \frac{3\left(\sqrt{2}-20\sqrt{3}\right)}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{4\left(12\sqrt{2}-2\sqrt{3}\right)-3\left(\sqrt{2}-20\sqrt{3}\right)}{12}$$

Mahia ngā whakarea i roto o 4\left(12\sqrt{2}-2\sqrt{3}\right)-3\left(\sqrt{2}-20\sqrt{3}\right).

$$\frac{48\sqrt{2}-8\sqrt{3}-3\sqrt{2}+60\sqrt{3}}{12}$$

Mahia ngā tātaitai i roto o 48\sqrt{2}-8\sqrt{3}-3\sqrt{2}+60\sqrt{3}.

$$\frac{45\sqrt{2}+52\sqrt{3}}{12}$$