Whakaoti i te sqrt{48}+6sqrt{1/3}-sqrt{75}

$$\sqrt { 48 } + 6 \sqrt { \frac { 1 } { 3 } } - \sqrt { 75 }$$

Aromātai

$$\sqrt{3}\approx 1.732050808$$

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}.

$$4\sqrt{3}+6\sqrt{\frac{1}{3}}-\sqrt{75}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$4\sqrt{3}+6\times \frac{\sqrt{1}}{\sqrt{3}}-\sqrt{75}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$4\sqrt{3}+6\times \frac{1}{\sqrt{3}}-\sqrt{75}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$4\sqrt{3}+6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{75}$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\sqrt{3}+6\times \frac{\sqrt{3}}{3}-\sqrt{75}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 6 me te 3.

$$4\sqrt{3}+2\sqrt{3}-\sqrt{75}$$

Pahekotia te 4\sqrt{3} me 2\sqrt{3}, ka 6\sqrt{3}.

$$6\sqrt{3}-\sqrt{75}$$

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}.

$$6\sqrt{3}-5\sqrt{3}$$

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

$$\sqrt{3}$$