Integrated Algebra –
Name
NOTES: Adding & Subtracting Radical Expressions
Date
Today’s Objectives
 Practice simplifying square-root expressions.
 Understand the difference between like and unlike radicals.
 Add and subtract square-root expressions.
Square root expressions with the
Like Radicals
Unlike Radicals
are examples of
2 5 and 4 5
2 and
15
6 x and -2 x
3 4t and
6 x and
3 2 and 2 3
6x
4t
Radicals are added in the same way that we add expressions with variables.
2x + 5 x = 7 x
Examples: Add or subtract the following square-root expressions.
1. 3 7 + 8 7
2. 9 y -
y
3. 12 2 - 4 11
4. -8 3d + 6 2d + 10 3d
Practice: Add or subtract the following.
1. 5 13 - 6 13
2. 8 3 - 5 3
3. 4 n + 4 n
4.
2s -
5s + 9 5s
Sometimes, radicals do not appear to be like until they are simplified. Simplify all
radicals in an expression before trying to identify like radicals.
Examples: Simplify the following expressions.
1.
12 +
27
2. 3 8 +
45
3. 5 28x - 8 7x
Practice: Simplify the following expressions.
1.
54 +
24
2. 4 27 -
18
3.
125b + 3 20b -
45b
Geometry Application
Find the perimeter of the triangle below. Express your answer as a radical expression in
simplest form.