Solve sqrt{0.25/548}

$$\sqrt { \frac { 0.25 } { 548 } }$$

Evaluate

$$\frac{\sqrt{137}}{548}\approx 0.021358941$$

Solution Steps

Expand \frac{0.25}{548} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{25}{54800}}$$

Reduce the fraction \frac{25}{54800} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{1}{2192}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2192}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2192}}.

$$\frac{\sqrt{1}}{\sqrt{2192}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2192}}$$

Factor 2192=4^{2}\times 137. Rewrite the square root of the product \sqrt{4^{2}\times 137} as the product of square roots \sqrt{4^{2}}\sqrt{137}. Take the square root of 4^{2}.

$$\frac{1}{4\sqrt{137}}$$

Rationalize the denominator of \frac{1}{4\sqrt{137}} by multiplying numerator and denominator by \sqrt{137}.

$$\frac{\sqrt{137}}{4\left(\sqrt{137}\right)^{2}}$$

The square of \sqrt{137} is 137.

$$\frac{\sqrt{137}}{4\times 137}$$

Multiply 4 and 137 to get 548.

$$\frac{\sqrt{137}}{548}$$