Algebra 1 Common Core Student Edition, Grade 8-9

m

The diagram labels

tw o im p ortant

featu res. W h at is

th e third?

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1

Getting Ready! ["«► X UL m

A pole 1 6 f t t a l l b r e a k s , as show n in t h e

d ia g r a m. W h a t is a n e x p r e s s io n f o r d in

term s o f h? Explain your process.

1

J

h ft

Ji

n

1— — d f t----------H

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