Question

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

Answer 1

It would be -2.

Explanation:

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

3 +
`√(11\\)` is your expression. The conjugate is an important concept you need to know to solve this.

Given the expression:
`a + √(b\\)`

It's conjugate would be:
`a - √(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+ √(11)` would be
`3 - √(11)`

2) Now we would have to multiply them

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

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