Solve (sqrt{7}+3)^2-(3-sqrt{7})

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

Evaluate

$$7\sqrt{7}+13\approx 31.520259177$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+3\right)^{2}.

$$\left(\sqrt{7}\right)^{2}+6\sqrt{7}+9-\left(3-\sqrt{7}\right)$$

The square of \sqrt{7} is 7.

$$7+6\sqrt{7}+9-\left(3-\sqrt{7}\right)$$

Add 7 and 9 to get 16.

$$16+6\sqrt{7}-\left(3-\sqrt{7}\right)$$

To find the opposite of 3-\sqrt{7}, find the opposite of each term.

$$16+6\sqrt{7}-3+\sqrt{7}$$

Subtract 3 from 16 to get 13.

$$13+6\sqrt{7}+\sqrt{7}$$

Combine 6\sqrt{7} and \sqrt{7} to get 7\sqrt{7}.

$$13+7\sqrt{7}$$