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

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

Evaluate

$$1$$

Solution Steps

Consider \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}.

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

The square of \sqrt{3} is 3.

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

The square of \sqrt{2} is 2.

$$\sqrt{3-2}$$

Subtract 2 from 3 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$