The name given to $8 - \sqrt{3}$ when rationalizing the denominator of $8 + \sqrt{3}$ is the conjugate.

The conjugate of a binomial expression $a + b$ (where $b$ includes a square root) is $a - b$, and multiplying by the conjugate helps eliminate the square root in the denominator.

Would you like a detailed explanation of how this works?

Here are five related questions to deepen your understanding:

1. What is the conjugate of $5 - \sqrt{7}$?
2. Why does multiplying by the conjugate help in rationalizing denominators?
3. How do you simplify $\frac{1}{3 + 2\sqrt{5}}$ using the conjugate?
4. What happens when you multiply $(a + b)$ by $(a - b)$?
5. Can conjugates be used in complex number arithmetic?

Tip: The product of conjugates follows the difference of squares formula:
$(a + b)(a - b) = a^2 - b^2$
This is why the square root term disappears when multiplying by the conjugate.