Solve sqrt{2/6}*sqrt{3/6}

$$\sqrt{ \frac{ 2 }{ 6 } } \times \sqrt{ \frac{ 3 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{6}}{6}\approx 0.40824829$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{3}}\sqrt{\frac{3}{6}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{1}}{\sqrt{3}}\sqrt{\frac{3}{6}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}\sqrt{\frac{3}{6}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\sqrt{3}}{3}\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{\sqrt{3}}{3}\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{3}}{3}\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply \frac{\sqrt{3}}{3} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\sqrt{6}}{3\times 2}$$

Multiply 3 and 2 to get 6.

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