Solve sqrt{6.67*10^-11*1.99*10^30/6.48*10^10}

$$\sqrt { \frac { 6.67 \times 10 ^ { - 11 } \times 1.99 \times 10 ^ { 30 } } { 6.48 \times 10 ^ { 10 } } }$$

Evaluate

$$\frac{500\sqrt{663665}}{9}\approx 45258.687181933$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$\sqrt{\frac{6.67\times 10^{19}\times 1.99}{6.48\times 10^{10}}}$$

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

$$\sqrt{\frac{1.99\times 6.67\times 10^{9}}{6.48}}$$

Multiply 1.99 and 6.67 to get 13.2733.

$$\sqrt{\frac{13.2733\times 10^{9}}{6.48}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\sqrt{\frac{13.2733\times 1000000000}{6.48}}$$

Multiply 13.2733 and 1000000000 to get 13273300000.

$$\sqrt{\frac{13273300000}{6.48}}$$

Expand \frac{13273300000}{6.48} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1327330000000}{648}}$$

Reduce the fraction \frac{1327330000000}{648} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{165916250000}{81}}$$

Rewrite the square root of the division \sqrt{\frac{165916250000}{81}} as the division of square roots \frac{\sqrt{165916250000}}{\sqrt{81}}.

$$\frac{\sqrt{165916250000}}{\sqrt{81}}$$

Factor 165916250000=500^{2}\times 663665. Rewrite the square root of the product \sqrt{500^{2}\times 663665} as the product of square roots \sqrt{500^{2}}\sqrt{663665}. Take the square root of 500^{2}.

$$\frac{500\sqrt{663665}}{\sqrt{81}}$$

Calculate the square root of 81 and get 9.

$$\frac{500\sqrt{663665}}{9}$$