Solve sqrt{2(6.21*10^-21)/5.31*10^-26}

$$\sqrt { \frac { 2 ( 6.21 \times 10 ^ { - 21 } ) } { 5.31 \times 10 ^ { - 26 } } }$$

Evaluate

$$\frac{200\sqrt{20355}}{59}\approx 483.630339293$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\sqrt{\frac{2\times 6.21\times 10^{5}}{5.31}}$$

Multiply 2 and 6.21 to get 12.42.

$$\sqrt{\frac{12.42\times 10^{5}}{5.31}}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{12.42\times 100000}{5.31}}$$

Multiply 12.42 and 100000 to get 1242000.

$$\sqrt{\frac{1242000}{5.31}}$$

Expand \frac{1242000}{5.31} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{124200000}{531}}$$

Reduce the fraction \frac{124200000}{531} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{13800000}{59}}$$

Rewrite the square root of the division \sqrt{\frac{13800000}{59}} as the division of square roots \frac{\sqrt{13800000}}{\sqrt{59}}.

$$\frac{\sqrt{13800000}}{\sqrt{59}}$$

Factor 13800000=200^{2}\times 345. Rewrite the square root of the product \sqrt{200^{2}\times 345} as the product of square roots \sqrt{200^{2}}\sqrt{345}. Take the square root of 200^{2}.

$$\frac{200\sqrt{345}}{\sqrt{59}}$$

Rationalize the denominator of \frac{200\sqrt{345}}{\sqrt{59}} by multiplying numerator and denominator by \sqrt{59}.

$$\frac{200\sqrt{345}\sqrt{59}}{\left(\sqrt{59}\right)^{2}}$$

The square of \sqrt{59} is 59.

$$\frac{200\sqrt{345}\sqrt{59}}{59}$$

To multiply \sqrt{345} and \sqrt{59}, multiply the numbers under the square root.

$$\frac{200\sqrt{20355}}{59}$$