Properties of radicals

1. PROPERTIES OF RADICALS
n am

2. 1. Simplifying radicals
n· p am· p = n· p am· p = n am
Example:
8 36 = 4 33

3. 2. Root of a product
n a·b = n a·n b
Example:
3 3x = 3 3·3 x

4. Consequence 1: taking factors out
4 24·3 = 4 24 ·4 3 = 2·4 3

5. Consequence 2: multiplying roots with the same index
3 24 ·3 22 = 3 24·22 = 3 26 = 22

6. 3. Root of a quotient
n a :b = n a : n b
Example:
3
6
y
=
3
3
6
y

7. 4. Power of a root
( )m
n a = n am
Example:
( )5
3 2 =3 25

8. 5. Root of a root
m n a = m·n a
Example:
3 2 = 2·3 2 = 6 2