Solve sqrt{3*6.626*10^-34/8*9.1*10^-28*2*10^14}

$$\sqrt{ \frac{ 3 \times 6.626 \times { 10 }^{ -34 } }{ 8 \times 9.1 \times { 10 }^{ -28 } \times 2 \times { 10 }^{ 14 } } }$$

Evaluate

$$\frac{\sqrt{1808898}}{36400000000000}\approx 3.69492524 \cdot 10^{-11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -28 and 14 to get -14.

$$\sqrt{\frac{3\times 6.626\times 10^{-34}}{8\times 9.1\times 10^{-14}\times 2}}$$

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

$$\sqrt{\frac{3\times 6.626}{2\times 8\times 9.1\times 10^{20}}}$$

Multiply 3 and 6.626 to get 19.878.

$$\sqrt{\frac{19.878}{2\times 8\times 9.1\times 10^{20}}}$$

Multiply 2 and 8 to get 16.

$$\sqrt{\frac{19.878}{16\times 9.1\times 10^{20}}}$$

Multiply 16 and 9.1 to get 145.6.

$$\sqrt{\frac{19.878}{145.6\times 10^{20}}}$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\sqrt{\frac{19.878}{145.6\times 100000000000000000000}}$$

Multiply 145.6 and 100000000000000000000 to get 14560000000000000000000.

$$\sqrt{\frac{19.878}{14560000000000000000000}}$$

Expand \frac{19.878}{14560000000000000000000} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{19878}{14560000000000000000000000}}$$

Reduce the fraction \frac{19878}{14560000000000000000000000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{9939}{7280000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{9939}{7280000000000000000000000}} as the division of square roots \frac{\sqrt{9939}}{\sqrt{7280000000000000000000000}}.

$$\frac{\sqrt{9939}}{\sqrt{7280000000000000000000000}}$$

Factor 7280000000000000000000000=200000000000^{2}\times 182. Rewrite the square root of the product \sqrt{200000000000^{2}\times 182} as the product of square roots \sqrt{200000000000^{2}}\sqrt{182}. Take the square root of 200000000000^{2}.

$$\frac{\sqrt{9939}}{200000000000\sqrt{182}}$$

Rationalize the denominator of \frac{\sqrt{9939}}{200000000000\sqrt{182}} by multiplying numerator and denominator by \sqrt{182}.

$$\frac{\sqrt{9939}\sqrt{182}}{200000000000\left(\sqrt{182}\right)^{2}}$$

The square of \sqrt{182} is 182.

$$\frac{\sqrt{9939}\sqrt{182}}{200000000000\times 182}$$

To multiply \sqrt{9939} and \sqrt{182}, multiply the numbers under the square root.

$$\frac{\sqrt{1808898}}{200000000000\times 182}$$

Multiply 200000000000 and 182 to get 36400000000000.

$$\frac{\sqrt{1808898}}{36400000000000}$$