Solve sqrt{1/7776}

$$\sqrt{ \frac{ 1 }{ 7776 } }$$

Evaluate

$$\frac{\sqrt{6}}{216}\approx 0.01134023$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{7776}} as the division of square roots \frac{\sqrt{1}}{\sqrt{7776}}.

$$\frac{\sqrt{1}}{\sqrt{7776}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{7776}}$$

Factor 7776=36^{2}\times 6. Rewrite the square root of the product \sqrt{36^{2}\times 6} as the product of square roots \sqrt{36^{2}}\sqrt{6}. Take the square root of 36^{2}.

$$\frac{1}{36\sqrt{6}}$$

Rationalize the denominator of \frac{1}{36\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{6}}{36\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

Multiply 36 and 6 to get 216.

$$\frac{\sqrt{6}}{216}$$