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

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

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{3}}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{\sqrt{3}}{3\times 2}\sqrt{3} as a single fraction.

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

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

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

Multiply 3 and 2 to get 6.

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

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$