Page 727 - Algebra 1

L E S S O N Solving Radical Equations 106
Warm Up
1. Vocabulary Which of the following expressions is a radical expression? (61)
A2x+4 Simplify.
2. (√ 5)2 (76)
Solve.
4.x2 +5x+6=0
(98)
B√ x+ 1+2 Cx2+5 3. (√ x + 2)2
(76)
5.x2 -5x=14 (98)
D2x2+3x+6
New Concepts An equation containing a variable in a radicand is called a radical equation. Inverse operations are used to solve radical equations. The inverse of finding
the square root of a term is squaring the term.
Solving Simple Radical Equations
Solve each equation.
a. √x =7 SOLUTION
Use inverse operations.
Square both sides. Simplify.
b. √ 4x = 12 SOLUTION
Use inverse operations.
Math Language
Inverse operations are operations that undo each other.
Example
1
√ x = 7 (√x)2 = 72

x = 49
Check √x =7 √ 4 9 7
7=7 ✓
Math Reasoning
Verify Show that simplifying √ 4x before squaring will result in the same solution.
712 Saxon Algebra 1
√ 4 x = 1 2 (√4 x)2 = 122
Square both sides. Simplify.
Division Property of Equality Simplify.
4x = 144 4x = 144
__ 44
x = 36