Whakaoti i te 4:(sqrt{48}+1/4sqrt{12})divsqrt{27}=

$$4 : ( \sqrt { 48 } + \frac { 1 } { 4 } \sqrt { 12 } ) \div \sqrt { 27 } =$$

Aromātai

$$\frac{8}{81}\approx 0.098765432$$

Ngā Upane Otinga

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{4}\sqrt{12}}}{\sqrt{27}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{4}\times 2\sqrt{3}}}{\sqrt{27}}$$

Whakareatia te \frac{1}{4} ki te 2, ka \frac{2}{4}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{2}{4}\sqrt{3}}}{\sqrt{27}}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{2}\sqrt{3}}}{\sqrt{27}}$$

Pahekotia te 4\sqrt{3} me \frac{1}{2}\sqrt{3}, ka \frac{9}{2}\sqrt{3}.

$$\frac{\frac{4}{\frac{9}{2}\sqrt{3}}}{\sqrt{27}}$$

Whakangāwaritia te tauraro o \frac{4}{\frac{9}{2}\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\frac{4\sqrt{3}}{\frac{9}{2}\left(\sqrt{3}\right)^{2}}}{\sqrt{27}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{4\sqrt{3}}{\frac{9}{2}\times 3}}{\sqrt{27}}$$

Tuhia te \frac{9}{2}\times 3 hei hautanga kotahi.

$$\frac{\frac{4\sqrt{3}}{\frac{9\times 3}{2}}}{\sqrt{27}}$$

Whakareatia te 9 ki te 3, ka 27.

$$\frac{\frac{4\sqrt{3}}{\frac{27}{2}}}{\sqrt{27}}$$

Whakawehe 4\sqrt{3} ki te \frac{27}{2} mā te whakarea 4\sqrt{3} ki te tau huripoki o \frac{27}{2}.

$$\frac{\frac{4\sqrt{3}\times 2}{27}}{\sqrt{27}}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{\frac{8\sqrt{3}}{27}}{\sqrt{27}}$$

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}.

$$\frac{\frac{8\sqrt{3}}{27}}{3\sqrt{3}}$$

Tuhia te \frac{\frac{8\sqrt{3}}{27}}{3\sqrt{3}} hei hautanga kotahi.

$$\frac{8\sqrt{3}}{27\times 3\sqrt{3}}$$

Me whakakore tahi te \sqrt{3} i te taurunga me te tauraro.

$$\frac{8}{3\times 27}$$

Whakareatia te 3 ki te 27, ka 81.

$$\frac{8}{81}$$

Tauwehe

$$\frac{2 ^ {3}}{3 ^ {4}} = 0.09876543209876543$$