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

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

Evaluate

$$3$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

The square of \sqrt{6} is 6.

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

The square of \sqrt{3} is 3.

$$6-3$$

Subtract 3 from 6 to get 3.

$$3$$

Factor

$$3$$