Solve sqrt{3*6.626*10^-34/8*9.1*10^-28*2*1.1^4}

$$\sqrt { \frac { 3 \times 6.626 \times 10 ^ { - 34 } } { 8 \times 9.1 \times 10 ^ { - 28 } \times 2 \times 1.1 ^ { 4 } } }$$

Evaluate

$$\frac{\sqrt{1808898}}{4404400}\approx 0.000305366$$

Solution Steps

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

$$\sqrt{\frac{3\times 6.626}{2\times 8\times 9.1\times 1.1^{4}\times 10^{6}}}$$

Multiply 3 and 6.626 to get 19.878.

$$\sqrt{\frac{19.878}{2\times 8\times 9.1\times 1.1^{4}\times 10^{6}}}$$

Multiply 2 and 8 to get 16.

$$\sqrt{\frac{19.878}{16\times 9.1\times 1.1^{4}\times 10^{6}}}$$

Multiply 16 and 9.1 to get 145.6.

$$\sqrt{\frac{19.878}{145.6\times 1.1^{4}\times 10^{6}}}$$

Calculate 1.1 to the power of 4 and get 1.4641.

$$\sqrt{\frac{19.878}{145.6\times 1.4641\times 10^{6}}}$$

Multiply 145.6 and 1.4641 to get 213.17296.

$$\sqrt{\frac{19.878}{213.17296\times 10^{6}}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt{\frac{19.878}{213.17296\times 1000000}}$$

Multiply 213.17296 and 1000000 to get 213172960.

$$\sqrt{\frac{19.878}{213172960}}$$

Expand \frac{19.878}{213172960} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{19878}{213172960000}}$$

Reduce the fraction \frac{19878}{213172960000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{9939}{106586480000}}$$

Rewrite the square root of the division \sqrt{\frac{9939}{106586480000}} as the division of square roots \frac{\sqrt{9939}}{\sqrt{106586480000}}.

$$\frac{\sqrt{9939}}{\sqrt{106586480000}}$$

Factor 106586480000=24200^{2}\times 182. Rewrite the square root of the product \sqrt{24200^{2}\times 182} as the product of square roots \sqrt{24200^{2}}\sqrt{182}. Take the square root of 24200^{2}.

$$\frac{\sqrt{9939}}{24200\sqrt{182}}$$

Rationalize the denominator of \frac{\sqrt{9939}}{24200\sqrt{182}} by multiplying numerator and denominator by \sqrt{182}.

$$\frac{\sqrt{9939}\sqrt{182}}{24200\left(\sqrt{182}\right)^{2}}$$

The square of \sqrt{182} is 182.

$$\frac{\sqrt{9939}\sqrt{182}}{24200\times 182}$$

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

$$\frac{\sqrt{1808898}}{24200\times 182}$$

Multiply 24200 and 182 to get 4404400.

$$\frac{\sqrt{1808898}}{4404400}$$