Solve frac{3sqrt{6}}{2sqrt{3}}

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

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Rationalize the denominator of \frac{3\sqrt{6}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{2}}{6}$$

Divide 9\sqrt{2} by 6 to get \frac{3}{2}\sqrt{2}.

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