Solve [sqrt{7}+sqrt{3})(sqrt{3}-sqrt{7})+sqrt{16}

$$[ \sqrt { 7 } + \sqrt { 3 } ) ( \sqrt { 3 } - \sqrt { 7 } ) + \sqrt { 16 }$$

Evaluate

$$0$$

Solution Steps

Consider \left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{3}-\sqrt{7}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{3}\right)^{2}-\left(\sqrt{7}\right)^{2}+\sqrt{16}$$

The square of \sqrt{3} is 3.

$$3-\left(\sqrt{7}\right)^{2}+\sqrt{16}$$

The square of \sqrt{7} is 7.

$$3-7+\sqrt{16}$$

Subtract 7 from 3 to get -4.

$$-4+\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$-4+4$$

Add -4 and 4 to get 0.

$$0$$

Factor

$$0$$