Solve frac{sqrt{15}}{3sqrt{6}}

$$\frac{ \sqrt{ 15 } }{ 3 \sqrt{ 6 } }$$

Evaluate

$$\frac{\sqrt{10}}{6}\approx 0.527046277$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{15}}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{15}\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{15}\sqrt{6}}{3\times 6}$$

To multiply \sqrt{15} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{90}}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{\sqrt{90}}{18}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{3\sqrt{10}}{18}$$

Divide 3\sqrt{10} by 18 to get \frac{1}{6}\sqrt{10}.

$$\frac{1}{6}\sqrt{10}$$