Solve sqrt{1/600}=

$$\sqrt{ \frac{ 1 }{ 600 } } =$$

Evaluate

$$\frac{\sqrt{6}}{60}\approx 0.040824829$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{600}} as the division of square roots \frac{\sqrt{1}}{\sqrt{600}}.

$$\frac{\sqrt{1}}{\sqrt{600}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{600}}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$\frac{1}{10\sqrt{6}}$$

Rationalize the denominator of \frac{1}{10\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{6}}{10\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{6}}{10\times 6}$$

Multiply 10 and 6 to get 60.

$$\frac{\sqrt{6}}{60}$$