Whakaoti i te (sqrt{2}-2)^2+sqrt{12/3}divsqrt{5/24}

$$( \sqrt { 2 } - 2 ) ^ { 2 } + \sqrt { 1 \frac { 2 } { 3 } } \div \sqrt { \frac { 5 } { 24 } }$$

Aromātai

$$6-2\sqrt{2}\approx 3.171572875$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{2}-2\right)^{2}.

$$\left(\sqrt{2}\right)^{2}-4\sqrt{2}+4+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$2-4\sqrt{2}+4+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

Tāpirihia te 2 ki te 4, ka 6.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

Whakareatia te 1 ki te 3, ka 3.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

Tāpirihia te 3 ki te 2, ka 5.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{5}{3}}}{\sqrt{\frac{5}{24}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{3}}.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}}{\sqrt{3}}}{\sqrt{\frac{5}{24}}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{5}{24}}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}\sqrt{3}}{3}}{\sqrt{\frac{5}{24}}}$$

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{5}{24}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{5}{24}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{5}}{\sqrt{24}}.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{\sqrt{24}}}$$

Tauwehea te 24=2^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 6} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{6}. Tuhia te pūtakerua o te 2^{2}.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{2\sqrt{6}}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{5}}{2\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{2\times 6}}$$

Hei whakarea \sqrt{5} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{2\times 6}}$$

Whakareatia te 2 ki te 6, ka 12.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{12}}$$

Whakawehe \frac{\sqrt{15}}{3} ki te \frac{\sqrt{30}}{12} mā te whakarea \frac{\sqrt{15}}{3} ki te tau huripoki o \frac{\sqrt{30}}{12}.

$$6-4\sqrt{2}+\frac{\sqrt{15}\times 12}{3\sqrt{30}}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$6-4\sqrt{2}+\frac{4\sqrt{15}}{\sqrt{30}}$$

Whakangāwaritia te tauraro o \frac{4\sqrt{15}}{\sqrt{30}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{30}.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

Ko te pūrua o \sqrt{30} ko 30.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{30}}{30}$$

Tauwehea te 30=15\times 2. Tuhia anō te pūtake rua o te hua \sqrt{15\times 2} hei hua o ngā pūtake rua \sqrt{15}\sqrt{2}.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{15}\sqrt{2}}{30}$$

Whakareatia te \sqrt{15} ki te \sqrt{15}, ka 15.

$$6-4\sqrt{2}+\frac{4\times 15\sqrt{2}}{30}$$

Whakareatia te 4 ki te 15, ka 60.

$$6-4\sqrt{2}+\frac{60\sqrt{2}}{30}$$

Whakawehea te 60\sqrt{2} ki te 30, kia riro ko 2\sqrt{2}.

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

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

$$6-2\sqrt{2}$$