Whakaoti i te 5sqrt{700}-4sqrt{343}-3sqrt{112}-21sqrt{7^-1}

$$5 \sqrt{ 700 } -4 \sqrt{ 343 } -3 \sqrt{ 112 } -21 \sqrt{ { 7 }^{ -1 } }$$

Aromātai

$$7\sqrt{7}\approx 18.520259177$$

Ngā Upane Otinga

Tauwehea te 700=10^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{10^{2}\times 7} hei hua o ngā pūtake rua \sqrt{10^{2}}\sqrt{7}. Tuhia te pūtakerua o te 10^{2}.

$$5\times 10\sqrt{7}-4\sqrt{343}-3\sqrt{112}-21\sqrt{7^{-1}}$$

Whakareatia te 5 ki te 10, ka 50.

$$50\sqrt{7}-4\sqrt{343}-3\sqrt{112}-21\sqrt{7^{-1}}$$

Tauwehea te 343=7^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 7} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{7}. Tuhia te pūtakerua o te 7^{2}.

$$50\sqrt{7}-4\times 7\sqrt{7}-3\sqrt{112}-21\sqrt{7^{-1}}$$

Whakareatia te -4 ki te 7, ka -28.

$$50\sqrt{7}-28\sqrt{7}-3\sqrt{112}-21\sqrt{7^{-1}}$$

Pahekotia te 50\sqrt{7} me -28\sqrt{7}, ka 22\sqrt{7}.

$$22\sqrt{7}-3\sqrt{112}-21\sqrt{7^{-1}}$$

Tauwehea te 112=4^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 7} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{7}. Tuhia te pūtakerua o te 4^{2}.

$$22\sqrt{7}-3\times 4\sqrt{7}-21\sqrt{7^{-1}}$$

Whakareatia te -3 ki te 4, ka -12.

$$22\sqrt{7}-12\sqrt{7}-21\sqrt{7^{-1}}$$

Pahekotia te 22\sqrt{7} me -12\sqrt{7}, ka 10\sqrt{7}.

$$10\sqrt{7}-21\sqrt{7^{-1}}$$

Tātaihia te 7 mā te pū o -1, kia riro ko \frac{1}{7}.

$$10\sqrt{7}-21\sqrt{\frac{1}{7}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{7}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{7}}.

$$10\sqrt{7}-21\times \frac{\sqrt{1}}{\sqrt{7}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$10\sqrt{7}-21\times \frac{1}{\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}.

$$10\sqrt{7}-21\times \frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$10\sqrt{7}-21\times \frac{\sqrt{7}}{7}$$

Whakakorea atu te tauwehe pūnoa nui rawa 7 i roto i te 21 me te 7.

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

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

$$7\sqrt{7}$$