Whakaoti i te sqrt{588}-sqrt{300}+sqrt{108}-21sqrt{3^-1}

$$\sqrt{ 588 } - \sqrt{ 300 } + \sqrt{ 108 } -21 \sqrt{ { 3 }^{ -1 } }$$

Aromātai

$$3\sqrt{3}\approx 5.196152423$$

Ngā Upane Otinga

Tauwehea te 588=14^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{14^{2}\times 3} hei hua o ngā pūtake rua \sqrt{14^{2}}\sqrt{3}. Tuhia te pūtakerua o te 14^{2}.

$$14\sqrt{3}-\sqrt{300}+\sqrt{108}-21\sqrt{3^{-1}}$$

Tauwehea te 300=10^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{10^{2}\times 3} hei hua o ngā pūtake rua \sqrt{10^{2}}\sqrt{3}. Tuhia te pūtakerua o te 10^{2}.

$$14\sqrt{3}-10\sqrt{3}+\sqrt{108}-21\sqrt{3^{-1}}$$

Pahekotia te 14\sqrt{3} me -10\sqrt{3}, ka 4\sqrt{3}.

$$4\sqrt{3}+\sqrt{108}-21\sqrt{3^{-1}}$$

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}.

$$4\sqrt{3}+6\sqrt{3}-21\sqrt{3^{-1}}$$

Pahekotia te 4\sqrt{3} me 6\sqrt{3}, ka 10\sqrt{3}.

$$10\sqrt{3}-21\sqrt{3^{-1}}$$

Tātaihia te 3 mā te pū o -1, kia riro ko \frac{1}{3}.

$$10\sqrt{3}-21\sqrt{\frac{1}{3}}$$

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

$$10\sqrt{3}-21\times \frac{\sqrt{1}}{\sqrt{3}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$10\sqrt{3}-21\times \frac{1}{\sqrt{3}}$$

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

$$10\sqrt{3}-21\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$10\sqrt{3}-21\times \frac{\sqrt{3}}{3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 21 me te 3.

$$10\sqrt{3}-7\sqrt{3}$$

Pahekotia te 10\sqrt{3} me -7\sqrt{3}, ka 3\sqrt{3}.

$$3\sqrt{3}$$