Question

Find the product of $5-\sqrt{6}$ with its conjugate pair.

• A. $5$
• B. $6$
• C. $19$
• D. $31$

Answer 1

The correct option is C $19$

The conjugate of $5-\sqrt{6}$ is $5+\sqrt{6}$
By using $(a^2-b^2)=(a+b)(a-b)$
$\therefore$ The product is $(5-\sqrt{6})\times (5+\sqrt{6})=5^2-(\sqrt{6}{)}^2=25-6=19$.

Therefore, option $C$ is correct.