Solve sqrt{2*4800/6.022*10^23*0.28}

$$\sqrt { \frac { 2 \times 4800 } { 6.022 \times 10 ^ { 23 } \times 0.28 } }$$

Evaluate

$$\frac{\sqrt{63231}}{1053850000000}\approx 2.386086729 \cdot 10^{-10}$$

Solution Steps

Multiply 2 and 4800 to get 9600.

$$\sqrt{\frac{9600}{6.022\times 10^{23}\times 0.28}}$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\sqrt{\frac{9600}{6.022\times 100000000000000000000000\times 0.28}}$$

Multiply 6.022 and 100000000000000000000000 to get 602200000000000000000000.

$$\sqrt{\frac{9600}{602200000000000000000000\times 0.28}}$$

Multiply 602200000000000000000000 and 0.28 to get 168616000000000000000000.

$$\sqrt{\frac{9600}{168616000000000000000000}}$$

Reduce the fraction \frac{9600}{168616000000000000000000} to lowest terms by extracting and canceling out 3200.

$$\sqrt{\frac{3}{52692500000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{52692500000000000000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{52692500000000000000}}.

$$\frac{\sqrt{3}}{\sqrt{52692500000000000000}}$$

Factor 52692500000000000000=50000000^{2}\times 21077. Rewrite the square root of the product \sqrt{50000000^{2}\times 21077} as the product of square roots \sqrt{50000000^{2}}\sqrt{21077}. Take the square root of 50000000^{2}.

$$\frac{\sqrt{3}}{50000000\sqrt{21077}}$$

Rationalize the denominator of \frac{\sqrt{3}}{50000000\sqrt{21077}} by multiplying numerator and denominator by \sqrt{21077}.

$$\frac{\sqrt{3}\sqrt{21077}}{50000000\left(\sqrt{21077}\right)^{2}}$$

The square of \sqrt{21077} is 21077.

$$\frac{\sqrt{3}\sqrt{21077}}{50000000\times 21077}$$

To multiply \sqrt{3} and \sqrt{21077}, multiply the numbers under the square root.

$$\frac{\sqrt{63231}}{50000000\times 21077}$$

Multiply 50000000 and 21077 to get 1053850000000.

$$\frac{\sqrt{63231}}{1053850000000}$$