Solve sqrt{0.032*10^-7}

$$\sqrt{ 0.032 \times { 10 }^{ -7 } }$$

Evaluate

$$\frac{\sqrt{2}}{25000}\approx 0.000056569$$

Solution Steps

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\sqrt{0.032\times \frac{1}{10000000}}$$

Multiply 0.032 and \frac{1}{10000000} to get \frac{1}{312500000}.

$$\sqrt{\frac{1}{312500000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{312500000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{312500000}}.

$$\frac{\sqrt{1}}{\sqrt{312500000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{312500000}}$$

Factor 312500000=12500^{2}\times 2. Rewrite the square root of the product \sqrt{12500^{2}\times 2} as the product of square roots \sqrt{12500^{2}}\sqrt{2}. Take the square root of 12500^{2}.

$$\frac{1}{12500\sqrt{2}}$$

Rationalize the denominator of \frac{1}{12500\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{12500\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{12500\times 2}$$

Multiply 12500 and 2 to get 25000.

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