Solve 1(sqrt{2}+sqrt{3})(sqrt{3}-sqrt{2})

$$1 ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 3 } - \sqrt { 2 } )$$

Evaluate

$$1$$

Solution Steps

Use the distributive property to multiply 1 by \sqrt{2}+\sqrt{3}.

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

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

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

The square of \sqrt{3} is 3.

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

The square of \sqrt{2} is 2.

$$3-2$$

Subtract 2 from 3 to get 1.

$$1$$

Factor

$$1$$