Whakaoti i te sqrt{6.67*10^-11*1.99*10^30/4.59*10^10}

$$\sqrt { \frac { 6.67 \times 10 ^ { - 11 } \times 1.99 \times 10 ^ { 30 } } { 4.59 \times 10 ^ { 10 } } }$$

Aromātai

$$\frac{1000\sqrt{67693830}}{153}\approx 53775.333493849$$

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -11 me te 30 kia riro ai te 19.

$$\sqrt{\frac{6.67\times 10^{19}\times 1.99}{4.59\times 10^{10}}}$$

Me whakakore tahi te 10^{10} i te taurunga me te tauraro.

$$\sqrt{\frac{1.99\times 6.67\times 10^{9}}{4.59}}$$

Whakareatia te 1.99 ki te 6.67, ka 13.2733.

$$\sqrt{\frac{13.2733\times 10^{9}}{4.59}}$$

Tātaihia te 10 mā te pū o 9, kia riro ko 1000000000.

$$\sqrt{\frac{13.2733\times 1000000000}{4.59}}$$

Whakareatia te 13.2733 ki te 1000000000, ka 13273300000.

$$\sqrt{\frac{13273300000}{4.59}}$$

Whakarohaina te \frac{13273300000}{4.59} mā te whakarea i te taurunga me te tauraro ki te 100.

$$\sqrt{\frac{1327330000000}{459}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1327330000000}{459}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1327330000000}}{\sqrt{459}}.

$$\frac{\sqrt{1327330000000}}{\sqrt{459}}$$

Tauwehea te 1327330000000=1000^{2}\times 1327330. Tuhia anō te pūtake rua o te hua \sqrt{1000^{2}\times 1327330} hei hua o ngā pūtake rua \sqrt{1000^{2}}\sqrt{1327330}. Tuhia te pūtakerua o te 1000^{2}.

$$\frac{1000\sqrt{1327330}}{\sqrt{459}}$$

Tauwehea te 459=3^{2}\times 51. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 51} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{51}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{1000\sqrt{1327330}}{3\sqrt{51}}$$

Whakangāwaritia te tauraro o \frac{1000\sqrt{1327330}}{3\sqrt{51}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{51}.

$$\frac{1000\sqrt{1327330}\sqrt{51}}{3\left(\sqrt{51}\right)^{2}}$$

Ko te pūrua o \sqrt{51} ko 51.

$$\frac{1000\sqrt{1327330}\sqrt{51}}{3\times 51}$$

Hei whakarea \sqrt{1327330} me \sqrt{51}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{1000\sqrt{67693830}}{3\times 51}$$

Whakareatia te 3 ki te 51, ka 153.

$$\frac{1000\sqrt{67693830}}{153}$$