Distribute 2sqrt(3) into the first parenthesis.

a) Simplify $2\sqrt{3}(2-\sqrt{3}) + 2\sqrt{2}(\sqrt{2}-1)$ Step 1: Distribute $2\sqrt{3}$ into the first parenthesis. $$ 2\sqrt{3}(2-\sqrt{3}) = (2\sqrt{3} \times 2) - (2\sqrt{3} \times \sqrt{3}) $$ $$ = 4\sqrt{3} - 2(\sqrt{3 \times 3}) $$ $$ = 4\sqrt{3} - 2(3) $$ $$ = 4\sqrt{3} - 6 $$ Step 2: Distribute $2\sqrt{2}$ into the second parenthesis. $$ 2\sqrt{2}(\sqrt{2}-1) = (2\sqrt{2} \times \sqrt{2}) - (2\sqrt{2} \times 1) $$ $$ = 2(\sqrt{2 \times 2}) - 2\sqrt{2} $$ $$ = 2(2) - 2\sqrt{2} $$ $$ = 4 - 2\sqrt{2} $$ Step 3: Combine the simplified expressions. $$ (4\sqrt{3} - 6) + (4 - 2\sqrt{2}) $$ $$ = 4\sqrt{3} - 6 + 4 - 2\sqrt{2} $$ Combine the constant terms: $$ = 4\sqrt{3} - 2\sqrt{2} - 2 $$ The simplified expression is $\boxed{4\sqrt{3} - 2\sqrt{2} - 2}$. b) Hence evaluate your answer in (a) correct to 2dp given that $\sqrt{2} = 1.414$ and $\sqrt{3} = 1.732$ Step 1: Substitute the given values of $\sqrt{2}$ and $\sqrt{3}$ into the simplified expression from part (a). $$ 4\sqrt{3} - 2\sqrt{2} - 2 = 4(1.732) - 2(1.414) - 2 $$ Step 2: Perform the multiplications. $$ 4 \times 1.732 = 6.928 $$ $$ 2 \times 1.414 = 2.828 $$ Step 3: Perform the subtractions. $$ 6.928 - 2.828 - 2 $$ $$ = 4.100 - 2 $$ $$ = 2.100 $$ Step 4: Round the result to 2 decimal places. $$ 2.100 \approx 2.10 $$ The evaluated answer is $\boxed{2.10}$. 3 done, 2 left today. You're making progress.