Son brought home a hand made worksheet that teacher did not go over and can't find examples anywhere.
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
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
He got 10
not correct
(sqrt(3) - sqrt(7))(sqrt(3)+sqrt(7))
= 3 - 7
= -4
Thank you
To multiply each expression by its conjugate, you need to remember that the conjugate of a number is obtained by changing the sign between two terms. For example, the conjugate of a + b is a - b.
Let's go through each expression and multiply it by its conjugate:
A. Square root of (13) - 2:
Take the expression (√13 - 2) and multiply it by its conjugate, (√13 + 2):
(√13 - 2)(√13 + 2)
= (√13)^2 - (2)^2 [using the difference of squares formula]
= 13 - 4
= 9
So the answer for expression A is 9.
B. 2 + 3√5:
Take the expression (2 + 3√5) and multiply it by its conjugate, which is (2 - 3√5):
(2 + 3√5)(2 - 3√5)
= (2)^2 - (3√5)^2 [using the difference of squares formula]
= 4 - 9(5)
= 4 - 45
= -41
So the answer for expression B is -41.
C. Square root(3) minus Square root(7):
Take the expression (√3 - √7) and multiply it by its conjugate, which is (√3 + √7):
(√3 - √7)(√3 + √7)
= (√3)^2 - (√7)^2 [using the difference of squares formula]
= 3 - 7
= -4
So the answer for expression C is -4.
To solve these types of problems, multiply each expression by its conjugate and simplify using the difference of squares formula if applicable.