Solve sqrt{(6.67*10^-11)*(6*10^24)/6600}

$$\sqrt{ \frac{ (6.67 \times { 10 }^{ -11 } ) \times (6 \times { 10 }^{ 24 } ) }{ 6600 } }$$

Evaluate

$$\frac{10000\sqrt{73370}}{11}\approx 246244.52001286$$

Solution Steps

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

$$\sqrt{\frac{6.67\times 10^{13}\times 6}{6600}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt{\frac{6.67\times 10000000000000\times 6}{6600}}$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$\sqrt{\frac{66700000000000\times 6}{6600}}$$

Multiply 66700000000000 and 6 to get 400200000000000.

$$\sqrt{\frac{400200000000000}{6600}}$$

Reduce the fraction \frac{400200000000000}{6600} to lowest terms by extracting and canceling out 600.

$$\sqrt{\frac{667000000000}{11}}$$

Rewrite the square root of the division \sqrt{\frac{667000000000}{11}} as the division of square roots \frac{\sqrt{667000000000}}{\sqrt{11}}.

$$\frac{\sqrt{667000000000}}{\sqrt{11}}$$

Factor 667000000000=10000^{2}\times 6670. Rewrite the square root of the product \sqrt{10000^{2}\times 6670} as the product of square roots \sqrt{10000^{2}}\sqrt{6670}. Take the square root of 10000^{2}.

$$\frac{10000\sqrt{6670}}{\sqrt{11}}$$

Rationalize the denominator of \frac{10000\sqrt{6670}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{10000\sqrt{6670}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{10000\sqrt{6670}\sqrt{11}}{11}$$

To multiply \sqrt{6670} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{10000\sqrt{73370}}{11}$$