Solve 2/sqrt{300}

$$\frac { 2 } { \sqrt { 300 } }$$

Evaluate

$$\frac{\sqrt{3}}{15}\approx 0.115470054$$

Solution Steps

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$\frac{2}{10\sqrt{3}}$$

Rationalize the denominator of \frac{2}{10\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{3}}{10\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{10\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{3}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{\sqrt{3}}{15}$$