Solve sqrt{1/80}

$$\sqrt { \frac { 1 } { 80 } }$$

Evaluate

$$\frac{\sqrt{5}}{20}\approx 0.111803399$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{80}} as the division of square roots \frac{\sqrt{1}}{\sqrt{80}}.

$$\frac{\sqrt{1}}{\sqrt{80}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{80}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{1}{4\sqrt{5}}$$

Rationalize the denominator of \frac{1}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{\sqrt{5}}{20}$$