Solve sqrt{3}(-frac{sqrt{3}}{sqrt{2}})

$$\sqrt { 3 } ( - \frac { \sqrt { 3 } } { \sqrt { 2 } } )$$

Evaluate

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

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Express \sqrt{3}\left(-\frac{\sqrt{6}}{2}\right) as a single fraction.

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

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}.

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

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

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