Solve sqrt{6.67*10^-11*6*10^24/1500000}(1+0.333/1-0.33)

$$\sqrt { \frac { 6.67 \times 10 ^ { - 11 } \times 6 \times 10 ^ { 24 } } { 1500000 } } ( \frac { 1 + 0.333 } { 1 - 0.33 } )$$

Evaluate

$$\frac{26660\sqrt{6670}}{67}\approx 32497.373309211$$

Solution Steps

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

$$\sqrt{\frac{6.67\times 10^{13}\times 6}{1500000}}\times \frac{1+0.333}{1-0.33}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt{\frac{6.67\times 10000000000000\times 6}{1500000}}\times \frac{1+0.333}{1-0.33}$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$\sqrt{\frac{66700000000000\times 6}{1500000}}\times \frac{1+0.333}{1-0.33}$$

Multiply 66700000000000 and 6 to get 400200000000000.

$$\sqrt{\frac{400200000000000}{1500000}}\times \frac{1+0.333}{1-0.33}$$

Divide 400200000000000 by 1500000 to get 266800000.

$$\sqrt{266800000}\times \frac{1+0.333}{1-0.33}$$

Factor 266800000=200^{2}\times 6670. Rewrite the square root of the product \sqrt{200^{2}\times 6670} as the product of square roots \sqrt{200^{2}}\sqrt{6670}. Take the square root of 200^{2}.

$$200\sqrt{6670}\times \frac{1+0.333}{1-0.33}$$

Add 1 and 0.333 to get 1.333.

$$200\sqrt{6670}\times \frac{1.333}{1-0.33}$$

Subtract 0.33 from 1 to get 0.67.

$$200\sqrt{6670}\times \frac{1.333}{0.67}$$

Expand \frac{1.333}{0.67} by multiplying both numerator and the denominator by 1000.

$$200\sqrt{6670}\times \frac{1333}{670}$$

Multiply 200 and \frac{1333}{670} to get \frac{26660}{67}.

$$\frac{26660}{67}\sqrt{6670}$$