Answer:
It would be -2.
Step-by-step explanation:
Key skills: Conjugate, Distribution Property, and Addition/Subtraction
3 + [tex]\sqrt{11\\}[/tex] is your expression. The conjugate is an important concept you need to know to solve this.
Given the expression: [tex]a + \sqrt{b\\}[/tex]
It's conjugate would be: [tex]a - \sqrt{b}[/tex]
(Basically if there is an addition sign between the 2 terms, it would become a subtractions symbol and if there is a subtraction symbol it would become an addition symbol)
1) So the conjugate of [tex]3+ \sqrt{11}[/tex] would be [tex]3 - \sqrt{11}[/tex]
2) Now we would have to multiply them
- ([tex]3 + \sqrt{11}[/tex])([tex]3- \sqrt{11}[/tex]) is your expression.
- If you use distribution property, you will get to: [tex]3^{2} + 3\sqrt{11} - 3\sqrt{11} + \sqrt{11}^{2}[/tex]
- The two middle terms would cancel out (they both add up to 0), so then we have [tex]3^{2} - \sqrt{11}^2[/tex]
- This would simplify into 9-11, which is then -2
Hope you understood, and have a nice day!! :)
