Solve sqrt{4/3*55*10^-9*667*10^-11*314}

$$\sqrt { \frac { 4 } { 3 } \times 55 \times 10 ^ { - 9 } \times 667 \times 10 ^ { - 11 } \times 314 }$$

Evaluate

$$\frac{\sqrt{34557270}}{15000000000}\approx 0.000000392$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -11 to get -20.

$$\sqrt{\frac{4}{3}\times 55\times 10^{-20}\times 667\times 314}$$

Multiply \frac{4}{3} and 55 to get \frac{220}{3}.

$$\sqrt{\frac{220}{3}\times 10^{-20}\times 667\times 314}$$

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\sqrt{\frac{220}{3}\times \frac{1}{100000000000000000000}\times 667\times 314}$$

Multiply \frac{220}{3} and \frac{1}{100000000000000000000} to get \frac{11}{15000000000000000000}.

$$\sqrt{\frac{11}{15000000000000000000}\times 667\times 314}$$

Multiply \frac{11}{15000000000000000000} and 667 to get \frac{7337}{15000000000000000000}.

$$\sqrt{\frac{7337}{15000000000000000000}\times 314}$$

Multiply \frac{7337}{15000000000000000000} and 314 to get \frac{1151909}{7500000000000000000}.

$$\sqrt{\frac{1151909}{7500000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1151909}{7500000000000000000}} as the division of square roots \frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}.

$$\frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}$$

Factor 7500000000000000000=500000000^{2}\times 30. Rewrite the square root of the product \sqrt{500000000^{2}\times 30} as the product of square roots \sqrt{500000000^{2}}\sqrt{30}. Take the square root of 500000000^{2}.

$$\frac{\sqrt{1151909}}{500000000\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{1151909}}{500000000\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\times 30}$$

To multiply \sqrt{1151909} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{34557270}}{500000000\times 30}$$

Multiply 500000000 and 30 to get 15000000000.

$$\frac{\sqrt{34557270}}{15000000000}$$