Solve sqrt{3*10^17^/6.67*10^-11}

$$\sqrt{ \frac{ 3 \times { 10 }^{ { 17 }^{ } } }{ 6.67 \times { 10 }^{ -11 } } }$$

Evaluate

$$\frac{1000000000000000\sqrt{2001}}{667}\approx 6.70652751 \cdot 10^{13}$$

Solution Steps

Calculate 17 to the power of 1 and get 17.

$$\sqrt{\frac{3\times 10^{17}}{6.67\times 10^{-11}}}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\sqrt{\frac{3\times 100000000000000000}{6.67\times 10^{-11}}}$$

Multiply 3 and 100000000000000000 to get 300000000000000000.

$$\sqrt{\frac{300000000000000000}{6.67\times 10^{-11}}}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\sqrt{\frac{300000000000000000}{6.67\times \frac{1}{100000000000}}}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\sqrt{\frac{300000000000000000}{\frac{667}{10000000000000}}}$$

Divide 300000000000000000 by \frac{667}{10000000000000} by multiplying 300000000000000000 by the reciprocal of \frac{667}{10000000000000}.

$$\sqrt{300000000000000000\times \frac{10000000000000}{667}}$$

Multiply 300000000000000000 and \frac{10000000000000}{667} to get \frac{3000000000000000000000000000000}{667}.

$$\sqrt{\frac{3000000000000000000000000000000}{667}}$$

Rewrite the square root of the division \sqrt{\frac{3000000000000000000000000000000}{667}} as the division of square roots \frac{\sqrt{3000000000000000000000000000000}}{\sqrt{667}}.

$$\frac{\sqrt{3000000000000000000000000000000}}{\sqrt{667}}$$

Factor 3000000000000000000000000000000=1000000000000000^{2}\times 3. Rewrite the square root of the product \sqrt{1000000000000000^{2}\times 3} as the product of square roots \sqrt{1000000000000000^{2}}\sqrt{3}. Take the square root of 1000000000000000^{2}.

$$\frac{1000000000000000\sqrt{3}}{\sqrt{667}}$$

Rationalize the denominator of \frac{1000000000000000\sqrt{3}}{\sqrt{667}} by multiplying numerator and denominator by \sqrt{667}.

$$\frac{1000000000000000\sqrt{3}\sqrt{667}}{\left(\sqrt{667}\right)^{2}}$$

The square of \sqrt{667} is 667.

$$\frac{1000000000000000\sqrt{3}\sqrt{667}}{667}$$

To multiply \sqrt{3} and \sqrt{667}, multiply the numbers under the square root.

$$\frac{1000000000000000\sqrt{2001}}{667}$$