Solve sqrt{7,2*10^-10/0,1}

$$\sqrt { \frac { 7,2 \cdot 10 ^ { - 10 } } { 0,1 } }$$

Evaluate

$$\frac{3\sqrt{2}}{50000}\approx 0.000084853$$

Solution Steps

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\sqrt{\frac{7,2\times \frac{1}{10000000000}}{0,1}}$$

Multiply 7,2 and \frac{1}{10000000000} to get \frac{9}{12500000000}.

$$\sqrt{\frac{\frac{9}{12500000000}}{0,1}}$$

Express \frac{\frac{9}{12500000000}}{0,1} as a single fraction.

$$\sqrt{\frac{9}{12500000000\times 0,1}}$$

Multiply 12500000000 and 0,1 to get 1250000000.

$$\sqrt{\frac{9}{1250000000}}$$

Rewrite the square root of the division \sqrt{\frac{9}{1250000000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{1250000000}}.

$$\frac{\sqrt{9}}{\sqrt{1250000000}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{1250000000}}$$

Factor 1250000000=25000^{2}\times 2. Rewrite the square root of the product \sqrt{25000^{2}\times 2} as the product of square roots \sqrt{25000^{2}}\sqrt{2}. Take the square root of 25000^{2}.

$$\frac{3}{25000\sqrt{2}}$$

Rationalize the denominator of \frac{3}{25000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{25000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{25000\times 2}$$

Multiply 25000 and 2 to get 50000.

$$\frac{3\sqrt{2}}{50000}$$