Solve 5sqrt{3}+3sqrt{7}-[2sqrt{3}-(4sqrt{7}-3sqrt{3})]

$$5 \sqrt { 3 } + 3 \sqrt { 7 } - [ 2 \sqrt { 3 } - ( 4 \sqrt { 7 } - 3 \sqrt { 3 } ) ]$$

Evaluate

$$7\sqrt{7}\approx 18.520259177$$

Solution Steps

To find the opposite of 4\sqrt{7}-3\sqrt{3}, find the opposite of each term.

$$5\sqrt{3}+3\sqrt{7}-\left(2\sqrt{3}-4\sqrt{7}-\left(-3\sqrt{3}\right)\right)$$

The opposite of -3\sqrt{3} is 3\sqrt{3}.

$$5\sqrt{3}+3\sqrt{7}-\left(2\sqrt{3}-4\sqrt{7}+3\sqrt{3}\right)$$

Combine 2\sqrt{3} and 3\sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}+3\sqrt{7}-\left(5\sqrt{3}-4\sqrt{7}\right)$$

To find the opposite of 5\sqrt{3}-4\sqrt{7}, find the opposite of each term.

$$5\sqrt{3}+3\sqrt{7}-5\sqrt{3}-\left(-4\sqrt{7}\right)$$

Combine 5\sqrt{3} and -5\sqrt{3} to get 0.

$$3\sqrt{7}-\left(-4\sqrt{7}\right)$$

The opposite of -4\sqrt{7} is 4\sqrt{7}.

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

Combine 3\sqrt{7} and 4\sqrt{7} to get 7\sqrt{7}.

$$7\sqrt{7}$$