Question

Find the product of the 3+ V11 and its conjugate.

Answer 1

Answer:

It would be -2.

Step-by-step explanation:

Key skills: Conjugate, Distribution Property, and Addition/Subtraction

3 + $\sqrt{11\\}$ is your expression. The conjugate is an important concept you need to know to solve this.

Given the expression: $a + \sqrt{b\\}$

It's conjugate would be: $a - \sqrt{b}$

(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  $3+ \sqrt{11}$ would be $3 - \sqrt{11}$

2) Now we would have to multiply them

• ($3 + \sqrt{11}$)($3- \sqrt{11}$) is your expression.
• If you use distribution property, you will get to: $3^{2} + 3\sqrt{11} - 3\sqrt{11} + \sqrt{11}^{2}$
• The two middle terms would cancel out (they both add up to 0), so then we have $3^{2} - \sqrt{11}^2$
• This would simplify into 9-11, which is then -2

Hope you understood, and have a nice day!! :)