Solve sqrt{1/4500}

$$\sqrt { \frac { 1 } { 4500 } }$$

Evaluate

$$\frac{\sqrt{5}}{150}\approx 0.01490712$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{4500}} as the division of square roots \frac{\sqrt{1}}{\sqrt{4500}}.

$$\frac{\sqrt{1}}{\sqrt{4500}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{4500}}$$

Factor 4500=30^{2}\times 5. Rewrite the square root of the product \sqrt{30^{2}\times 5} as the product of square roots \sqrt{30^{2}}\sqrt{5}. Take the square root of 30^{2}.

$$\frac{1}{30\sqrt{5}}$$

Rationalize the denominator of \frac{1}{30\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{30\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{30\times 5}$$

Multiply 30 and 5 to get 150.

$$\frac{\sqrt{5}}{150}$$