Solve sqrt{1/216}

$$\sqrt{ \frac{ 1 }{ 216 } }$$

Evaluate

$$\frac{\sqrt{6}}{36}\approx 0.068041382$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{216}} as the division of square roots \frac{\sqrt{1}}{\sqrt{216}}.

$$\frac{\sqrt{1}}{\sqrt{216}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{216}}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$\frac{1}{6\sqrt{6}}$$

Rationalize the denominator of \frac{1}{6\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{6}}{6\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{6}}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{\sqrt{6}}{36}$$