Solve frac{sqrt{3}*sqrt{2}}{sqrt{30}}

$$\frac{ \sqrt{ 3 } \times \sqrt{ 2 } }{ \sqrt{ 30 } }$$

Evaluate

$$\frac{\sqrt{5}}{5}\approx 0.447213595$$

Solution Steps

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{6}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{6}\sqrt{30}}{30}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\frac{\sqrt{6}\sqrt{6}\sqrt{5}}{30}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6\sqrt{5}}{30}$$

Divide 6\sqrt{5} by 30 to get \frac{1}{5}\sqrt{5}.

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