Whakaoti i te 0.5sqrt{0.04+1/6}sqrt{144}

$$0.5 \sqrt{ 0.04+ \frac{ 1 }{ 6 } } \sqrt{ 144 }$$

Aromātai

$$\frac{\sqrt{186}}{5}\approx 2.727636339$$

Ngā Upane Otinga

Me tahuri ki tau ā-ira 0.04 ki te hautau \frac{4}{100}. Whakahekea te hautanga \frac{4}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$0.5\sqrt{\frac{1}{25}+\frac{1}{6}}\sqrt{144}$$

Ko te maha noa iti rawa atu o 25 me 6 ko 150. Me tahuri \frac{1}{25} me \frac{1}{6} ki te hautau me te tautūnga 150.

$$0.5\sqrt{\frac{6}{150}+\frac{25}{150}}\sqrt{144}$$

Tā te mea he rite te tauraro o \frac{6}{150} me \frac{25}{150}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$0.5\sqrt{\frac{6+25}{150}}\sqrt{144}$$

Tāpirihia te 6 ki te 25, ka 31.

$$0.5\sqrt{\frac{31}{150}}\sqrt{144}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{31}{150}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{31}}{\sqrt{150}}.

$$0.5\times \frac{\sqrt{31}}{\sqrt{150}}\sqrt{144}$$

Tauwehea te 150=5^{2}\times 6. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 6} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{6}. Tuhia te pūtakerua o te 5^{2}.

$$0.5\times \frac{\sqrt{31}}{5\sqrt{6}}\sqrt{144}$$

Whakangāwaritia te tauraro o \frac{\sqrt{31}}{5\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$0.5\times \frac{\sqrt{31}\sqrt{6}}{5\left(\sqrt{6}\right)^{2}}\sqrt{144}$$

Ko te pūrua o \sqrt{6} ko 6.

$$0.5\times \frac{\sqrt{31}\sqrt{6}}{5\times 6}\sqrt{144}$$

Hei whakarea \sqrt{31} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$0.5\times \frac{\sqrt{186}}{5\times 6}\sqrt{144}$$

Whakareatia te 5 ki te 6, ka 30.

$$0.5\times \frac{\sqrt{186}}{30}\sqrt{144}$$

Tātaitia te pūtakerua o 144 kia tae ki 12.

$$0.5\times \frac{\sqrt{186}}{30}\times 12$$

Whakareatia te 0.5 ki te 12, ka 6.

$$6\times \frac{\sqrt{186}}{30}$$

Whakakorea atu te tauwehe pūnoa nui rawa 30 i roto i te 6 me te 30.

$$\frac{\sqrt{186}}{5}$$