Math 203 – Intermediate Algebra
Professor Valdez
Section 7.3 – Addition and Subtraction of Radicals
I. Combining Like Radicals
Radicals are said to be like if they have the same index and radicand.
ie,
3
7 & 23 7
4
OR
x & −4 x
When adding and subtracting radicals, we simplify by combining like radical terms.
ie,
3
7 + 23 7 = 33 7
OR
4
x −4x =0
Example 1 Add or subtract as specified.
A. − 4 9 + 34 9
t 2 − 4 −5 t 2 − 4
C.
E.
4
B. 6 p + p − 2 p
D. 53 a − 23 b
7− 77
II. Combining Unlike Radicals
When combining unlike radicals, we simplify first and try to combine those that are like (if
possible).
Example 2 Combine.
A.
75 + 27
B. 9 4 2 + 4 4 96 − 4 32
C.
24 − 28 + 63
D.
3
27a7b3 −123 ab 3
Example 3 Let f (x) = 10x 16x 3 and g(x) = 2x x 3 . Find:
A. f (x) + g(x)
Example 4
B. g(x) − f (x)