Son brought home a hand made worksheet that teacher did not go over and can't find examples anywhere.

Question

Multiply each expression by its conjugate.
A. Square root of (13)-2
B. 2+3Square root (5)
C. Square root(3) minus Square root(7)

Thanks

Answer 1

When you multiply a binomial by its conjugate, you are duplicating the pattern of the difference of squares:
a^2 - b^2 = (a+b)(a-b)

so
(sqrt(13) - 2)(sqrt(13) + 2)
= 13 - 4
= 9

(2+3sqrt(5))(2-3sqrt(5))
= 4 - 45
= -41

try the last one, let me know what you get

Answer 2

He got 10

Answer 3

not correct

(sqrt(3) - sqrt(7))(sqrt(3)+sqrt(7))
= 3 - 7
= -4

Answer 4

Thank you