Solve frac{sqrt{3}-sqrt{2}}{2}*frac{sqrt{3}+sqrt{2}}{2}

$$\frac{ \sqrt{ 3 } - \sqrt{ 2 } }{ 2 } \times \frac{ \sqrt{ 3 } + \sqrt{ 2 } }{ 2 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Multiply \frac{\sqrt{3}-\sqrt{2}}{2} times \frac{\sqrt{3}+\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Consider \left(\sqrt{3}-\sqrt{2}\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}.

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

The square of \sqrt{3} is 3.

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

The square of \sqrt{2} is 2.

$$\frac{3-2}{2\times 2}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$