Solve sqrt{6.67*10^2-11*1.2*10^17/10}

$$\sqrt{ \frac{ 6.67 \times { 10 }^{ 2-11 } \times 1.2 \times { 10 }^{ 17 } }{ 10 } }$$

Evaluate

$$200\sqrt{2001}\approx 8946.507698538$$

Solution Steps

Subtract 11 from 2 to get -9.

$$\sqrt{\frac{6.67\times 10^{-9}\times 1.2\times 10^{17}}{10}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\sqrt{\frac{6.67\times \frac{1}{1000000000}\times 1.2\times 10^{17}}{10}}$$

Multiply 6.67 and \frac{1}{1000000000} to get \frac{667}{100000000000}.

$$\sqrt{\frac{\frac{667}{100000000000}\times 1.2\times 10^{17}}{10}}$$

Multiply \frac{667}{100000000000} and 1.2 to get \frac{2001}{250000000000}.

$$\sqrt{\frac{\frac{2001}{250000000000}\times 10^{17}}{10}}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\sqrt{\frac{\frac{2001}{250000000000}\times 100000000000000000}{10}}$$

Multiply \frac{2001}{250000000000} and 100000000000000000 to get 800400000.

$$\sqrt{\frac{800400000}{10}}$$

Divide 800400000 by 10 to get 80040000.

$$\sqrt{80040000}$$

Factor 80040000=200^{2}\times 2001. Rewrite the square root of the product \sqrt{200^{2}\times 2001} as the product of square roots \sqrt{200^{2}}\sqrt{2001}. Take the square root of 200^{2}.

$$200\sqrt{2001}$$