Solve =sqrt{6.39*10^-3/3390*10^3*6378*10^5/5.97*10^24}

$$= \sqrt { \frac { 6.39 \times 10 ^ { - 3 } } { 3390 \times 10 ^ { 3 } } \times \frac { 6378 \times 10 ^ { 5 } } { 5.97 \times 10 ^ { 24 } } }$$

Evaluate

$$\frac{\sqrt{10182968106}}{224870000000000000}\approx 4.487512506 \cdot 10^{-13}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\sqrt{\frac{6.39}{3390\times 10^{6}}\times \frac{6378\times 10^{5}}{5.97\times 10^{24}}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt{\frac{6.39}{3390\times 1000000}\times \frac{6378\times 10^{5}}{5.97\times 10^{24}}}$$

Multiply 3390 and 1000000 to get 3390000000.

$$\sqrt{\frac{6.39}{3390000000}\times \frac{6378\times 10^{5}}{5.97\times 10^{24}}}$$

Expand \frac{6.39}{3390000000} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{639}{339000000000}\times \frac{6378\times 10^{5}}{5.97\times 10^{24}}}$$

Reduce the fraction \frac{639}{339000000000} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{213}{113000000000}\times \frac{6378\times 10^{5}}{5.97\times 10^{24}}}$$

Cancel out 10^{5} in both numerator and denominator.

$$\sqrt{\frac{213}{113000000000}\times \frac{6378}{5.97\times 10^{19}}}$$

Calculate 10 to the power of 19 and get 10000000000000000000.

$$\sqrt{\frac{213}{113000000000}\times \frac{6378}{5.97\times 10000000000000000000}}$$

Multiply 5.97 and 10000000000000000000 to get 59700000000000000000.

$$\sqrt{\frac{213}{113000000000}\times \frac{6378}{59700000000000000000}}$$

Reduce the fraction \frac{6378}{59700000000000000000} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{213}{113000000000}\times \frac{1063}{9950000000000000000}}$$

Multiply \frac{213}{113000000000} and \frac{1063}{9950000000000000000} to get \frac{226419}{1124350000000000000000000000000}.

$$\sqrt{\frac{226419}{1124350000000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{226419}{1124350000000000000000000000000}} as the division of square roots \frac{\sqrt{226419}}{\sqrt{1124350000000000000000000000000}}.

$$\frac{\sqrt{226419}}{\sqrt{1124350000000000000000000000000}}$$

Factor 1124350000000000000000000000000=5000000000000^{2}\times 44974. Rewrite the square root of the product \sqrt{5000000000000^{2}\times 44974} as the product of square roots \sqrt{5000000000000^{2}}\sqrt{44974}. Take the square root of 5000000000000^{2}.

$$\frac{\sqrt{226419}}{5000000000000\sqrt{44974}}$$

Rationalize the denominator of \frac{\sqrt{226419}}{5000000000000\sqrt{44974}} by multiplying numerator and denominator by \sqrt{44974}.

$$\frac{\sqrt{226419}\sqrt{44974}}{5000000000000\left(\sqrt{44974}\right)^{2}}$$

The square of \sqrt{44974} is 44974.

$$\frac{\sqrt{226419}\sqrt{44974}}{5000000000000\times 44974}$$

To multiply \sqrt{226419} and \sqrt{44974}, multiply the numbers under the square root.

$$\frac{\sqrt{10182968106}}{5000000000000\times 44974}$$

Multiply 5000000000000 and 44974 to get 224870000000000000.

$$\frac{\sqrt{10182968106}}{224870000000000000}$$