19. Expand $$ (8-\sqrt{3})^{2} $$ giving your answer in form $$ a+b \sqrt{3} $$

Question

UpStudy AI · Accepted Answer

1. Start with the expression:
   $$
   (8-\sqrt{3})^{2}
   $$

2. Use the square of a binomial formula:
   $$
   (a-b)^2 = a^2 - 2ab + b^2
   $$
   Here, $$ a = 8 $$ and $$ b = \sqrt{3} $$.

3. Substitute the values into the formula:
   $$
   (8-\sqrt{3})^{2} = 8^2 - 2 \cdot 8 \cdot \sqrt{3} + (\sqrt{3})^2
   $$

4. Calculate each term:
   - $$ 8^2 = 64 $$
   - $$ -2 \cdot 8 \cdot \sqrt{3} = -16\sqrt{3} $$
   - $$ (\sqrt{3})^2 = 3 $$

5. Combine the computed values:
   $$
   64 - 16\sqrt{3} + 3 = 67 - 16\sqrt{3}
   $$

6. The answer in the form $$ a+b\sqrt{3} $$ is:
   $$
   67 - 16\sqrt{3}
   $$
$$ 67 - 16\sqrt{3} $$

19. Expand \( (8-\sqrt{3})^{2} \) giving your answer in form \( a+b \sqrt{3} \)