Solve sqrt{2*6.67*10^-11*9.14*10^-24/5112}

$$\sqrt { \frac { 2 \times 6.67 \times 10 ^ { - 11 } \times 9.14 \times 10 ^ { - 24 } } { 5112 } }$$

Evaluate

$$\frac{\sqrt{108210745}}{21300000000000000000000}\approx 4.883774356 \cdot 10^{-19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and -24 to get -35.

$$\sqrt{\frac{2\times 6.67\times 10^{-35}\times 9.14}{5112}}$$

Multiply 2 and 6.67 to get 13.34.

$$\sqrt{\frac{13.34\times 10^{-35}\times 9.14}{5112}}$$

Calculate 10 to the power of -35 and get \frac{1}{100000000000000000000000000000000000}.

$$\sqrt{\frac{13.34\times \frac{1}{100000000000000000000000000000000000}\times 9.14}{5112}}$$

Multiply 13.34 and \frac{1}{100000000000000000000000000000000000} to get \frac{667}{5000000000000000000000000000000000000}.

$$\sqrt{\frac{\frac{667}{5000000000000000000000000000000000000}\times 9.14}{5112}}$$

Multiply \frac{667}{5000000000000000000000000000000000000} and 9.14 to get \frac{304819}{250000000000000000000000000000000000000}.

$$\sqrt{\frac{\frac{304819}{250000000000000000000000000000000000000}}{5112}}$$

Express \frac{\frac{304819}{250000000000000000000000000000000000000}}{5112} as a single fraction.

$$\sqrt{\frac{304819}{250000000000000000000000000000000000000\times 5112}}$$

Multiply 250000000000000000000000000000000000000 and 5112 to get 1278000000000000000000000000000000000000000.

$$\sqrt{\frac{304819}{1278000000000000000000000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{304819}{1278000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{304819}}{\sqrt{1278000000000000000000000000000000000000000}}.

$$\frac{\sqrt{304819}}{\sqrt{1278000000000000000000000000000000000000000}}$$

Factor 1278000000000000000000000000000000000000000=60000000000000000000^{2}\times 355. Rewrite the square root of the product \sqrt{60000000000000000000^{2}\times 355} as the product of square roots \sqrt{60000000000000000000^{2}}\sqrt{355}. Take the square root of 60000000000000000000^{2}.

$$\frac{\sqrt{304819}}{60000000000000000000\sqrt{355}}$$

Rationalize the denominator of \frac{\sqrt{304819}}{60000000000000000000\sqrt{355}} by multiplying numerator and denominator by \sqrt{355}.

$$\frac{\sqrt{304819}\sqrt{355}}{60000000000000000000\left(\sqrt{355}\right)^{2}}$$

The square of \sqrt{355} is 355.

$$\frac{\sqrt{304819}\sqrt{355}}{60000000000000000000\times 355}$$

To multiply \sqrt{304819} and \sqrt{355}, multiply the numbers under the square root.

$$\frac{\sqrt{108210745}}{60000000000000000000\times 355}$$

Multiply 60000000000000000000 and 355 to get 21300000000000000000000.

$$\frac{\sqrt{108210745}}{21300000000000000000000}$$