Whakaoti i te frac{sqrt{75}-sqrt{108}+sqrt{27}}{3sqrt{12}}

$$\frac { \sqrt { 75 } - \sqrt { 108 } + \sqrt { 27 } } { 3 \sqrt { 12 } }$$

Aromātai

$$\frac{1}{3}\approx 0.333333333$$

Ngā Upane Otinga

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}.

$$\frac{5\sqrt{3}-\sqrt{108}+\sqrt{27}}{3\sqrt{12}}$$

Tauwehea te 108=6^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 3} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{3}. Tuhia te pūtakerua o te 6^{2}.

$$\frac{5\sqrt{3}-6\sqrt{3}+\sqrt{27}}{3\sqrt{12}}$$

Pahekotia te 5\sqrt{3} me -6\sqrt{3}, ka -\sqrt{3}.

$$\frac{-\sqrt{3}+\sqrt{27}}{3\sqrt{12}}$$

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}.

$$\frac{-\sqrt{3}+3\sqrt{3}}{3\sqrt{12}}$$

Pahekotia te -\sqrt{3} me 3\sqrt{3}, ka 2\sqrt{3}.

$$\frac{2\sqrt{3}}{3\sqrt{12}}$$

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}.

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

Whakareatia te 3 ki te 2, ka 6.

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

Me whakakore tahi te 2\sqrt{3} i te taurunga me te tauraro.

$$\frac{1}{3}$$

Tauwehe

$$\frac{1}{3} = 0.3333333333333333$$