Solve frac{3sqrt{5}}{2sqrt{3}}frac{sqrt{3}}{sqrt{3}}

$$\frac{ 3 \sqrt{ 5 } }{ 2 \sqrt{ 3 } } \frac{ \sqrt{ 3 } }{ \sqrt{ 3 } }$$

Evaluate

$$\frac{\sqrt{15}}{2}\approx 1.936491673$$

Solution Steps

Divide \sqrt{3} by \sqrt{3} to get 1.

$$\frac{3\sqrt{5}}{2\sqrt{3}}\times 1$$

Rationalize the denominator of \frac{3\sqrt{5}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3\sqrt{5}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\times 1$$

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{5}\sqrt{3}}{2\times 3}\times 1$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{3\sqrt{15}}{2\times 3}\times 1$$

Multiply 2 and 3 to get 6.

$$\frac{3\sqrt{15}}{6}\times 1$$

Divide 3\sqrt{15} by 6 to get \frac{1}{2}\sqrt{15}.

$$\frac{1}{2}\sqrt{15}\times 1$$

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

$$\frac{1}{2}\sqrt{15}$$