Solve 2/102*frac{sqrt{108}}{10}

$$\frac { 2 } { 102 } \times \frac { \sqrt { 108 } } { 10 }$$

Evaluate

$$\frac{\sqrt{3}}{85}\approx 0.020377068$$

Solution Steps

Reduce the fraction \frac{2}{102} to lowest terms by extracting and canceling out 2.

$$\frac{1}{51}\times \frac{\sqrt{108}}{10}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{1}{51}\times \frac{6\sqrt{3}}{10}$$

Divide 6\sqrt{3} by 10 to get \frac{3}{5}\sqrt{3}.

$$\frac{1}{51}\times \frac{3}{5}\sqrt{3}$$

Multiply \frac{1}{51} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{51\times 5}\sqrt{3}$$

Do the multiplications in the fraction \frac{1\times 3}{51\times 5}.

$$\frac{3}{255}\sqrt{3}$$

Reduce the fraction \frac{3}{255} to lowest terms by extracting and canceling out 3.

$$\frac{1}{85}\sqrt{3}$$