Solve sqrt{2}divsqrt{3}*1/sqrt{3}

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

Evaluate

$$\frac{\sqrt{2}}{3}\approx 0.471404521$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{1}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{6}}{3} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 3 and 3 to get 9.

$$\frac{3\sqrt{2}}{9}$$

Divide 3\sqrt{2} by 9 to get \frac{1}{3}\sqrt{2}.

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