Solve {l}{(sqrt{3}-2)^2}{+sqrt{2}+6sqrt{2}}

$$\left. \begin{array} { l } { ( \sqrt { 3 } - 2 ) ^ { 2 } } \\ { + \sqrt { 2 } + 6 \sqrt { 2 } } \end{array} \right.$$

Evaluate

$$7\sqrt{2}+7-4\sqrt{3}\approx 9.971291706$$

Solution Steps

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

$$\left(\sqrt{3}\right)^{2}-4\sqrt{3}+4+\sqrt{2}+6\sqrt{2}$$

The square of \sqrt{3} is 3.

$$3-4\sqrt{3}+4+\sqrt{2}+6\sqrt{2}$$

Add 3 and 4 to get 7.

$$7-4\sqrt{3}+\sqrt{2}+6\sqrt{2}$$

Combine \sqrt{2} and 6\sqrt{2} to get 7\sqrt{2}.

$$7-4\sqrt{3}+7\sqrt{2}$$