find conjucate of √5+√12+√5+√12/√5+√12-√5-√12
Answers
Answer:
What is the radical conjugate of
12
−
√
5
?
Algebra Multiplication and Division of Radicals
1 Answer
George C.
Jun 25, 2016
12
+
√
5
Explanation:
The conjugate of
12
−
√
5
is
12
+
√
5
.
This has the property that:
(
12
−
√
5
)
(
12
+
√
5
)
is rational:
(
12
−
√
5
)
(
12
+
√
5
)
=
12
2
−
(
√
5
)
2
=
144
−
5
=
139
Typical examples where you would use the conjugate would be:
When rationalising the denominator of a quotient.
When looking at zeros of a polynomial with rational (typically integer) coefficients.
For example:
2
+
3
√
5
12
−
√
5
=
(
2
+
3
√
5
)
(
12
+
√
5
)
(
12
−
√
5
)
(
12
+
√
5
)
=
24
+
2
√
5
+
36
√
5
+
15
144
−
5
=
39
+
38
√
5
139
The simplest polynomial with rational coefficients and zero
12
−
√
5
is:
(
x
−
(
12
−
√
5
)
)
(
x
−
(
12
+
√
5
)
)
=
x
2
−
24
x
+
139
Answer link
Related topic
Multiplication and Division of Radicals
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