Solve sqrt{1/31.784}

$$\sqrt{ \frac{ 1 }{ 31.784 } }$$

Evaluate

$$\frac{5\sqrt{19865}}{3973}\approx 0.177376354$$

Solution Steps

Expand \frac{1}{31.784} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1000}{31784}}$$

Reduce the fraction \frac{1000}{31784} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{125}{3973}}$$

Rewrite the square root of the division \sqrt{\frac{125}{3973}} as the division of square roots \frac{\sqrt{125}}{\sqrt{3973}}.

$$\frac{\sqrt{125}}{\sqrt{3973}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{5\sqrt{5}}{\sqrt{3973}}$$

Rationalize the denominator of \frac{5\sqrt{5}}{\sqrt{3973}} by multiplying numerator and denominator by \sqrt{3973}.

$$\frac{5\sqrt{5}\sqrt{3973}}{\left(\sqrt{3973}\right)^{2}}$$

The square of \sqrt{3973} is 3973.

$$\frac{5\sqrt{5}\sqrt{3973}}{3973}$$

To multiply \sqrt{5} and \sqrt{3973}, multiply the numbers under the square root.

$$\frac{5\sqrt{19865}}{3973}$$