Solve sqrt{(1300*10^6)/8*3.986*10^14}6378137

$$\sqrt { \frac { ( 1300 \times 10 ^ { 6 } ) } { 8 \times 3.986 \times 10 ^ { 14 } } } 6378137$$

Evaluate

$$\frac{6378137\sqrt{259090}}{797200}\approx 4072.413598539$$

Solution Steps

Cancel out 4\times 10^{6} in both numerator and denominator.

$$6378137\sqrt{\frac{325}{2\times 3.986\times 10^{8}}}$$

Multiply 2 and 3.986 to get 7.972.

$$6378137\sqrt{\frac{325}{7.972\times 10^{8}}}$$

Calculate 10 to the power of 8 and get 100000000.

$$6378137\sqrt{\frac{325}{7.972\times 100000000}}$$

Multiply 7.972 and 100000000 to get 797200000.

$$6378137\sqrt{\frac{325}{797200000}}$$

Reduce the fraction \frac{325}{797200000} to lowest terms by extracting and canceling out 25.

$$6378137\sqrt{\frac{13}{31888000}}$$

Rewrite the square root of the division \sqrt{\frac{13}{31888000}} as the division of square roots \frac{\sqrt{13}}{\sqrt{31888000}}.

$$6378137\times \frac{\sqrt{13}}{\sqrt{31888000}}$$

Factor 31888000=40^{2}\times 19930. Rewrite the square root of the product \sqrt{40^{2}\times 19930} as the product of square roots \sqrt{40^{2}}\sqrt{19930}. Take the square root of 40^{2}.

$$6378137\times \frac{\sqrt{13}}{40\sqrt{19930}}$$

Rationalize the denominator of \frac{\sqrt{13}}{40\sqrt{19930}} by multiplying numerator and denominator by \sqrt{19930}.

$$6378137\times \frac{\sqrt{13}\sqrt{19930}}{40\left(\sqrt{19930}\right)^{2}}$$

The square of \sqrt{19930} is 19930.

$$6378137\times \frac{\sqrt{13}\sqrt{19930}}{40\times 19930}$$

To multiply \sqrt{13} and \sqrt{19930}, multiply the numbers under the square root.

$$6378137\times \frac{\sqrt{259090}}{40\times 19930}$$

Multiply 40 and 19930 to get 797200.

$$6378137\times \frac{\sqrt{259090}}{797200}$$

Express 6378137\times \frac{\sqrt{259090}}{797200} as a single fraction.

$$\frac{6378137\sqrt{259090}}{797200}$$