Algebraic Manipulation Worksheets With Answers - Craven Community College Page 16
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29To simplify a fraction that has a binomial radical expression in the denominator, multiply the numerator
and denominator by the conjugate form of the denominator and simplify.
Example:
2
V
5 + 2
V
2
5 – 2
Multiply by the conjugate
V
V
5 + 2 •
5 – 2
V
2 (
5 – 2)
V
V
V
25 – 2
5 + 2
5 – 4
V
2 (
5 – 2)
5 – 4
V
2(
5 – 2)
Solving Equations with Radical Expressions
Equations that contain radicals can be solved by using the equality property of powers, which states that if
two real numbers are equal, then any natural power of these numbers is also equal. To use this property,
first isolate the radical on one side of the equation. Next raise both sides of the equation to the same
power and solve as usual. Always check all answers to eliminate “imposter roots” that may be introduced
by the squaring process.
3
V
Example:
X
+ 3X – 17 + 2 = X
2
V
X
+ 3X – 17 = X – 2
Isolate the radical
2
2
2
2
V
(
X
+ 3X – 17
)
= (X – 2)
Square both sides
2
2
X
+ 3X – 17 = X
– 4X + 4
FOIL
2
3X – 17 = -4X + 4
Subtract X
from both sides
7X = 21
Combine like terms
X = 3
Divide by 7
V
Example:
32 + 3(3) – 17 + 2 = 3
V
9 + 9 – 17 + 2 = 3
V
1 + 2 = 3
3 = 3
The root is true
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