Solve sqrt{3*6626*10^-34/8*91*10^-28*2*10^14}

$$\sqrt{ \frac{ 3 \times 6626 \times { 10 }^{ -34 } }{ 8 \times 91 \times { 10 }^{ -28 } \times 2 \times { 10 }^{ 14 } } }$$

Evaluate

$$\frac{\sqrt{1808898}}{3640000000000}\approx 3.69492524 \cdot 10^{-10}$$

Solution Steps

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

$$\sqrt{\frac{3\times 6626\times 10^{-34}}{8\times 91\times 10^{-14}\times 2}}$$

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{3\times 3313\times 10^{-34}}{2\times 4\times 91\times 10^{-14}}}$$

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

$$\sqrt{\frac{3\times 3313}{2\times 4\times 91\times 10^{20}}}$$

Multiply 3 and 3313 to get 9939.

$$\sqrt{\frac{9939}{2\times 4\times 91\times 10^{20}}}$$

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{9939}{8\times 91\times 10^{20}}}$$

Multiply 8 and 91 to get 728.

$$\sqrt{\frac{9939}{728\times 10^{20}}}$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\sqrt{\frac{9939}{728\times 100000000000000000000}}$$

Multiply 728 and 100000000000000000000 to get 72800000000000000000000.

$$\sqrt{\frac{9939}{72800000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{9939}{72800000000000000000000}} as the division of square roots \frac{\sqrt{9939}}{\sqrt{72800000000000000000000}}.

$$\frac{\sqrt{9939}}{\sqrt{72800000000000000000000}}$$

Factor 72800000000000000000000=20000000000^{2}\times 182. Rewrite the square root of the product \sqrt{20000000000^{2}\times 182} as the product of square roots \sqrt{20000000000^{2}}\sqrt{182}. Take the square root of 20000000000^{2}.

$$\frac{\sqrt{9939}}{20000000000\sqrt{182}}$$

Rationalize the denominator of \frac{\sqrt{9939}}{20000000000\sqrt{182}} by multiplying numerator and denominator by \sqrt{182}.

$$\frac{\sqrt{9939}\sqrt{182}}{20000000000\left(\sqrt{182}\right)^{2}}$$

The square of \sqrt{182} is 182.

$$\frac{\sqrt{9939}\sqrt{182}}{20000000000\times 182}$$

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

$$\frac{\sqrt{1808898}}{20000000000\times 182}$$

Multiply 20000000000 and 182 to get 3640000000000.

$$\frac{\sqrt{1808898}}{3640000000000}$$