Solve frac{sqrt{2(2.16*10^-19}}{9.11*10^-31}

$$\frac { \sqrt { 2 ( 2.16 \times 10 ^ { - 19 } } } { 9.11 \times 10 ^ { - 31 } }$$

Evaluate

$$\frac{120000000000000000000000\sqrt{30}}{911}\approx 7.214786707 \cdot 10^{20}$$

Solution Steps

Multiply 2 and 2.16 to get 4.32.

$$\frac{\sqrt{4.32\times 10^{-19}}}{9.11\times 10^{-31}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{\sqrt{4.32\times \frac{1}{10000000000000000000}}}{9.11\times 10^{-31}}$$

Multiply 4.32 and \frac{1}{10000000000000000000} to get \frac{27}{62500000000000000000}.

$$\frac{\sqrt{\frac{27}{62500000000000000000}}}{9.11\times 10^{-31}}$$

Rewrite the square root of the division \sqrt{\frac{27}{62500000000000000000}} as the division of square roots \frac{\sqrt{27}}{\sqrt{62500000000000000000}}.

$$\frac{\frac{\sqrt{27}}{\sqrt{62500000000000000000}}}{9.11\times 10^{-31}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{\frac{3\sqrt{3}}{\sqrt{62500000000000000000}}}{9.11\times 10^{-31}}$$

Factor 62500000000000000000=2500000000^{2}\times 10. Rewrite the square root of the product \sqrt{2500000000^{2}\times 10} as the product of square roots \sqrt{2500000000^{2}}\sqrt{10}. Take the square root of 2500000000^{2}.

$$\frac{\frac{3\sqrt{3}}{2500000000\sqrt{10}}}{9.11\times 10^{-31}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{2500000000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\frac{3\sqrt{3}\sqrt{10}}{2500000000\left(\sqrt{10}\right)^{2}}}{9.11\times 10^{-31}}$$

The square of \sqrt{10} is 10.

$$\frac{\frac{3\sqrt{3}\sqrt{10}}{2500000000\times 10}}{9.11\times 10^{-31}}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\frac{3\sqrt{30}}{2500000000\times 10}}{9.11\times 10^{-31}}$$

Multiply 2500000000 and 10 to get 25000000000.

$$\frac{\frac{3\sqrt{30}}{25000000000}}{9.11\times 10^{-31}}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{\frac{3\sqrt{30}}{25000000000}}{9.11\times \frac{1}{10000000000000000000000000000000}}$$

Multiply 9.11 and \frac{1}{10000000000000000000000000000000} to get \frac{911}{1000000000000000000000000000000000}.

$$\frac{\frac{3\sqrt{30}}{25000000000}}{\frac{911}{1000000000000000000000000000000000}}$$

Divide \frac{3\sqrt{30}}{25000000000} by \frac{911}{1000000000000000000000000000000000} by multiplying \frac{3\sqrt{30}}{25000000000} by the reciprocal of \frac{911}{1000000000000000000000000000000000}.

$$\frac{3\sqrt{30}\times 1000000000000000000000000000000000}{25000000000\times 911}$$

Cancel out 25000000000 in both numerator and denominator.

$$\frac{3\times 40000000000000000000000\sqrt{30}}{911}$$

Multiply 3 and 40000000000000000000000 to get 120000000000000000000000.

$$\frac{120000000000000000000000\sqrt{30}}{911}$$