Solve sqrt{6.67*10^-11*5.98*10^24*24*60*60/4*3.14}

$$\sqrt { \frac { 6.67 \times 10 ^ { - 11 } \times 5.98 \times 10 ^ { 24 } \times 24 \times 60 \times 60 } { 4 \times 3.14 } }$$

Evaluate

$$\frac{276000000\sqrt{887835}}{157}\approx 1656439432.142536402$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\sqrt{\frac{6.67\times 10^{13}\times 5.98\times 24\times 60\times 60}{4\times 3.14}}$$

Cancel out 4 in both numerator and denominator.

$$\sqrt{\frac{5.98\times 6\times 6.67\times 60\times 60\times 10^{13}}{3.14}}$$

Multiply 5.98 and 6 to get 35.88.

$$\sqrt{\frac{35.88\times 6.67\times 60\times 60\times 10^{13}}{3.14}}$$

Multiply 35.88 and 6.67 to get 239.3196.

$$\sqrt{\frac{239.3196\times 60\times 60\times 10^{13}}{3.14}}$$

Multiply 239.3196 and 60 to get 14359.176.

$$\sqrt{\frac{14359.176\times 60\times 10^{13}}{3.14}}$$

Multiply 14359.176 and 60 to get 861550.56.

$$\sqrt{\frac{861550.56\times 10^{13}}{3.14}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt{\frac{861550.56\times 10000000000000}{3.14}}$$

Multiply 861550.56 and 10000000000000 to get 8615505600000000000.

$$\sqrt{\frac{8615505600000000000}{3.14}}$$

Expand \frac{8615505600000000000}{3.14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{861550560000000000000}{314}}$$

Reduce the fraction \frac{861550560000000000000}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{430775280000000000000}{157}}$$

Rewrite the square root of the division \sqrt{\frac{430775280000000000000}{157}} as the division of square roots \frac{\sqrt{430775280000000000000}}{\sqrt{157}}.

$$\frac{\sqrt{430775280000000000000}}{\sqrt{157}}$$

Factor 430775280000000000000=276000000^{2}\times 5655. Rewrite the square root of the product \sqrt{276000000^{2}\times 5655} as the product of square roots \sqrt{276000000^{2}}\sqrt{5655}. Take the square root of 276000000^{2}.

$$\frac{276000000\sqrt{5655}}{\sqrt{157}}$$

Rationalize the denominator of \frac{276000000\sqrt{5655}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{276000000\sqrt{5655}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{276000000\sqrt{5655}\sqrt{157}}{157}$$

To multiply \sqrt{5655} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{276000000\sqrt{887835}}{157}$$