Addition and Subtraction of Radical Expressions
Arithmetic of Radical Expressions
When we add, subtract, and multiply expressions that involve radicals we do so just as we do arithmetic on polynomials. we use the distributive law, combine like terms and FOIL.
Example:
-
3(
- 
) + 4( +
)
= 3 -
3 + 4 +
4
= 7 +
-
(
- 
)2
= ()2 - 2
+ ()2
= 3 - 2
+ 5 = 8 - 2
Exercises:
Perform the indicated operations and simplify
-
(
-
)( + )
-
3(
+
5
)2
Rationalizing The Denominator
When we divide with radicals in the denominator, we multiply the numerator
and denominator by the conjugate root
Definition If
is and expression, then its conjugate is
|
Example
+
(
+ )( +
)
=
-
(
- )(
+ )
= 2 + 2 +
3
5 + 2
=
2 -
3
-1
= -5 - 2
Exercises
Rationalize the denominator
2 +
+
3
-
4
2
- 4
15 3
4 +
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