Solve 6sqrt{2}-sqrt{3}(6sqrt{2}+sqrt{3})

$$6 \sqrt { 2 } - \sqrt { 3 } ( 6 \sqrt { 2 } + \sqrt { 3 } )$$

Evaluate

$$3\left(2\sqrt{2}-2\sqrt{6}-1\right)\approx -9.211657082$$

Solution Steps

Use the distributive property to multiply \sqrt{3} by 6\sqrt{2}+\sqrt{3}.

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

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

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

The square of \sqrt{3} is 3.

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

To find the opposite of 6\sqrt{6}+3, find the opposite of each term.

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