Solve {l}{6+3sqrt{2}-[6+3}{-4+sqrt{5}]-8}

$$\left. \begin{array} { l } { 6 + 3 \sqrt { 2 } - [ 6 + 3 } \\ { - 4 + \sqrt { 5 } ] - 8 } \end{array} \right.$$

Evaluate

$$3\sqrt{2}-\sqrt{5}-7\approx -4.99342729$$

Solution Steps

Add 6 and 3 to get 9.

$$6+3\sqrt{2}-\left(9-4+\sqrt{5}\right)-8$$

Subtract 4 from 9 to get 5.

$$6+3\sqrt{2}-\left(5+\sqrt{5}\right)-8$$

To find the opposite of 5+\sqrt{5}, find the opposite of each term.

$$6+3\sqrt{2}-5-\sqrt{5}-8$$

Subtract 5 from 6 to get 1.

$$1+3\sqrt{2}-\sqrt{5}-8$$

Subtract 8 from 1 to get -7.

$$-7+3\sqrt{2}-\sqrt{5}$$