Whakaoti i te (sqrt{48+1/4}sqrt{6})divsqrt{27}

$$( \sqrt{ 48+ \frac{ 1 }{ 4 } } \sqrt{ 6 } ) \div \sqrt{ 27 }$$

Aromātai

$$\frac{\sqrt{386}}{6}\approx 3.274480451$$

Ngā Upane Otinga

Me tahuri te 48 ki te hautau \frac{192}{4}.

$$\frac{\sqrt{\frac{192}{4}+\frac{1}{4}}\sqrt{6}}{\sqrt{27}}$$

Tā te mea he rite te tauraro o \frac{192}{4} me \frac{1}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\sqrt{\frac{192+1}{4}}\sqrt{6}}{\sqrt{27}}$$

Tāpirihia te 192 ki te 1, ka 193.

$$\frac{\sqrt{\frac{193}{4}}\sqrt{6}}{\sqrt{27}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{193}{4}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{193}}{\sqrt{4}}.

$$\frac{\frac{\sqrt{193}}{\sqrt{4}}\sqrt{6}}{\sqrt{27}}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{\frac{\sqrt{193}}{2}\sqrt{6}}{\sqrt{27}}$$

Tuhia te \frac{\sqrt{193}}{2}\sqrt{6} hei hautanga kotahi.

$$\frac{\frac{\sqrt{193}\sqrt{6}}{2}}{\sqrt{27}}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\frac{\sqrt{193}\sqrt{6}}{2}}{3\sqrt{3}}$$

Tuhia te \frac{\frac{\sqrt{193}\sqrt{6}}{2}}{3\sqrt{3}} hei hautanga kotahi.

$$\frac{\sqrt{193}\sqrt{6}}{2\times 3\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{193}\sqrt{6}}{2\times 3\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\sqrt{193}\sqrt{6}\sqrt{3}}{2\times 3\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\sqrt{193}\sqrt{6}\sqrt{3}}{2\times 3\times 3}$$

Hei whakarea \sqrt{193} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{1158}\sqrt{3}}{2\times 3\times 3}$$

Tauwehea te 1158=3\times 386. Tuhia anō te pūtake rua o te hua \sqrt{3\times 386} hei hua o ngā pūtake rua \sqrt{3}\sqrt{386}.

$$\frac{\sqrt{3}\sqrt{386}\sqrt{3}}{2\times 3\times 3}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{3\sqrt{386}}{2\times 3\times 3}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{3\sqrt{386}}{6\times 3}$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{3\sqrt{386}}{18}$$

Whakawehea te 3\sqrt{386} ki te 18, kia riro ko \frac{1}{6}\sqrt{386}.

$$\frac{1}{6}\sqrt{386}$$