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Lesso n
Vocabulary
radical eq u a tio n
- e x tr a n e o u s
solution
MATHEMATICAL
PRACTICES ifte expression for d in the Solve It has a variable in a radicand. A radical equation
is an equation that has a variable in a radicand. Examples include Vx -5 = 3
and Vx - 2 = 1. To solve a radical equation, get the radical by itself on one side
of the equation. Then square both sides. The expression under the radical must be
nonnegative.
Esse n t i a l U n d e r st a n d i n g You can solve some radical equations by squaring
each side of the equation and testing the solutions.
Solving Radical
Equations
@ Common Core State Standards
A-R EI.A.2 Solve simple rational and radical equations
in one variable, and give examples showing how
extraneous solutions may arise.
MP 1, MP 2, MP 3, M P 4
Object ives To solve equations containing radicals
To identify extraneous solutions
Plan
How do you start
when solving a
radical equation?
Use th e p ro p e rtie s o f
equality to get the radical
by itself on one side o f
the equation.
Lf e/ Pr o b l em 1 ]So l v i n g b y I so l a t i n g t h e Ra d i c a l
What is the solution of \Zx + 7 = 16?
V x + 7 = 16
V x = 9 Get the radical by itself on one side of the equation.
(V x)2 = 92 Square each side.
x = 81 Simplify.
Check Vx + 7 = 16
V8l + 7 ± 16 Substitute 81 fo r x.
9 + 7 = 16
Go t I t? 1. What is the solution of V x - 5 = -2?
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Po w erAlg eb ra.com | Lesso n 10- 4 So l v i n g Ra d i c a l Eq u a t i o n s 633