Solve sqrt{(1300*10^6)/8*3986*10^14}6378137

$$\sqrt { \frac { ( 1300 \times 10 ^ { 6 } ) } { 8 \times 3986 \times 10 ^ { 14 } } } 6378137$$

Evaluate

$$\frac{6378137\sqrt{25909}}{7972000}\approx 128.781025456$$

Solution Steps

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

$$6378137\sqrt{\frac{325}{2\times 3986\times 10^{8}}}$$

Multiply 2 and 3986 to get 7972.

$$6378137\sqrt{\frac{325}{7972\times 10^{8}}}$$

Calculate 10 to the power of 8 and get 100000000.

$$6378137\sqrt{\frac{325}{7972\times 100000000}}$$

Multiply 7972 and 100000000 to get 797200000000.

$$6378137\sqrt{\frac{325}{797200000000}}$$

Reduce the fraction \frac{325}{797200000000} to lowest terms by extracting and canceling out 25.

$$6378137\sqrt{\frac{13}{31888000000}}$$

Rewrite the square root of the division \sqrt{\frac{13}{31888000000}} as the division of square roots \frac{\sqrt{13}}{\sqrt{31888000000}}.

$$6378137\times \frac{\sqrt{13}}{\sqrt{31888000000}}$$

Factor 31888000000=4000^{2}\times 1993. Rewrite the square root of the product \sqrt{4000^{2}\times 1993} as the product of square roots \sqrt{4000^{2}}\sqrt{1993}. Take the square root of 4000^{2}.

$$6378137\times \frac{\sqrt{13}}{4000\sqrt{1993}}$$

Rationalize the denominator of \frac{\sqrt{13}}{4000\sqrt{1993}} by multiplying numerator and denominator by \sqrt{1993}.

$$6378137\times \frac{\sqrt{13}\sqrt{1993}}{4000\left(\sqrt{1993}\right)^{2}}$$

The square of \sqrt{1993} is 1993.

$$6378137\times \frac{\sqrt{13}\sqrt{1993}}{4000\times 1993}$$

To multiply \sqrt{13} and \sqrt{1993}, multiply the numbers under the square root.

$$6378137\times \frac{\sqrt{25909}}{4000\times 1993}$$

Multiply 4000 and 1993 to get 7972000.

$$6378137\times \frac{\sqrt{25909}}{7972000}$$

Express 6378137\times \frac{\sqrt{25909}}{7972000} as a single fraction.

$$\frac{6378137\sqrt{25909}}{7972000}$$