Solve 3.14/sqrt{2700}

$$\frac{ 3.14 }{ \sqrt{ 2700 } }$$

Evaluate

$$\frac{157\sqrt{3}}{4500}\approx 0.060429328$$

Solution Steps

Factor 2700=30^{2}\times 3. Rewrite the square root of the product \sqrt{30^{2}\times 3} as the product of square roots \sqrt{30^{2}}\sqrt{3}. Take the square root of 30^{2}.

$$\frac{3.14}{30\sqrt{3}}$$

Rationalize the denominator of \frac{3.14}{30\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3.14\sqrt{3}}{30\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3.14\sqrt{3}}{30\times 3}$$

Multiply 30 and 3 to get 90.

$$\frac{3.14\sqrt{3}}{90}$$

Divide 3.14\sqrt{3} by 90 to get \frac{157}{4500}\sqrt{3}.

$$\frac{157}{4500}\sqrt{3}$$