Solve sqrt{2.512/3.14*8}

$$\sqrt{ \frac{ 2.512 }{ 3.14 \times 8 } }$$

Evaluate

$$\frac{\sqrt{10}}{10}\approx 0.316227766$$

Solution Steps

Multiply 3.14 and 8 to get 25.12.

$$\sqrt{\frac{2.512}{25.12}}$$

Expand \frac{2.512}{25.12} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{2512}{25120}}$$

Reduce the fraction \frac{2512}{25120} to lowest terms by extracting and canceling out 2512.

$$\sqrt{\frac{1}{10}}$$

Rewrite the square root of the division \sqrt{\frac{1}{10}} as the division of square roots \frac{\sqrt{1}}{\sqrt{10}}.

$$\frac{\sqrt{1}}{\sqrt{10}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{10}}$$

Rationalize the denominator of \frac{1}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{10}}{10}$$