Simplifying Radical
Expressions
Simplifying Radicals
Radicals with variables
Definition of Square Root: For any real
numbers a and b, if a2 = b, then a is a
Radical
square root of b.
sign
Index
number
k
a
radicand
Radical Expression
Let’s review. Simplify each expression.
Assume all values of the variable are positive.
Examples:
(1). 3 54
 3 96
3 9 6
 33 6
9 6
Examples:
(2).
125 p
3
 25  p  5  p
2
 25 p  5 p
2
 5p 5p
Try these with your partner:
(3).
100n
3
 100  n  n
2
 100n  n
2
 10n n
Try these with your partner:
(4).
2
5y
5y
2


5y
5y

2 5y
25 y
2
2 5y

5y
Adding and Subtracting
Radical Expressions
Radical expressions can be combined (added or
subtracted) if they are like radicals – that is, they
have the same root ________
index and the same
________.
radicand
Example 5: 6 and 5 6 are alike. The root
index is _____
2 for both expressions and the
radicand is _____
6 for both expressions.
3
Example 6: 4 x and 4x are not alike. They
both have the same __________
radicand but the root
indices are not the same.
_______
To determine whether two radicals are like
simplify each
radicals, you must first __________
radicand.
Simplify each expression:
(7).
3 6  7 6  10 6
(8).
8 7 2 7 6 7
(9).
(10).
2  5 2 15 2
 9 2
3 7 5 6 3 2 5
 3  6 3  7 5  2 5  5 3  9 5
Try these with your partner:
(11).
4 11  2 11  9 11  3 11
(12). 5 x 3  7 x 3  2x 3
(13). 6 7  9 2  11 7
 5 7  9 2
(14). 9 13  4 10  6 10  3 13
 9 13  3 13  4 10  6 10
 12 13  10 10
Add or subtract as indicated. Simplify first!
(15). 7 5  4 45
 7 5  4 95
 7 5  4 9  5
 7 5  4  3 5
 7 5  12 5
 19 5
(16).
2 50  12 8
 2 25  2  12 4  2
 2 25  2  12 4  2
 2  5  2 12  2  2
 10 2  24 2
 14 2
Try these with your partner:
(17).
2 2  18
 2 2  92
2 2 9 2
 2 2 3 2
5 2
(18).
4 27  2 75
 4 9  3  2 25  3
 4 9  3  2 25  3
 4  3 3  2  5 3
 12 3  10 3
2 3
(19).
 2 9 y  10 y
 2 9  y  10 y
 2 9  y  10 y
 2  3  y  10 y
 6 y  10 y
4 y
(20).
5 80 x  7 20 x
 5 16  5x  7 4  5x
 5 16  5x  7 4  5x
 5  4  5x  7  2  5x
 20 5 x  14 5 x
 6 5x