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

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

Evaluate

$$3\left(\sqrt{6}+1\right)\approx 10.348469228$$

Solution Steps

Combine 2\sqrt{3} and -\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}\left(3\sqrt{2}+\sqrt{3}\right)$$

Use the distributive property to multiply \sqrt{3} by 3\sqrt{2}+\sqrt{3}.

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

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

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

The square of \sqrt{3} is 3.

$$3\sqrt{6}+3$$

Factor

$$3 {(\sqrt{6} + 1)} = 10.348469228$$