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

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

Evaluate

$$1$$

Solution Steps

The square of \sqrt{2} is 2.

$$\left(2-\frac{1}{2}\times 2\sqrt{3}\right)\left(2+\sqrt{3}\right)$$

Multiply \frac{1}{2} and 2 to get 1.

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

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

$$4-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$4-3$$

Subtract 3 from 4 to get 1.

$$1$$

Factor

$$1$$