Name _____________________________________________________
Simplifying Radicals
Date _____________
CCA2 Per___________
A __________________________ is one which contains a root (square root, cube root, etc.)
Simplifying Radicals
A radical is in simplest form when:
 the radicand contains no perfect square, cube, etc. factors
Perfect Squares:
Perfect Cubes:
 the radicand is not a fraction
 there are no radicals in the denominator of a fraction.
Simplifying Radical Expressions
Ex. 1:
75
1. Find the largest perfect square, cube, etc. that is a factor of the radicand
(depending on the index)
2. Re-write the radicand as the product of the largest perfect square, cube,
etc. and its other factor

3. Simplify the perfect square, cube, etc.
Ex. 2:
5 3 16
1. Find the largest perfect square, cube, etc. that is a factor of the radicand
(depending on the index)
2. Re-write the radicand as the product of the largest perfect square, cube,
etc. and its other factor
3. Simplify the perfect square, cube, etc.
Practice: Simplify each radical.
Ex. 3: 8 27
Ex. 4: 3 3 48
Ex. 5: 2 x 3  54
Simplifying Radicals with Variables:
b17
Ex. 6:
1. Find the largest perfect power,
depending on the index, that can be
factored out. (Must be divisible by the index)
2. Re-write using the new powers
3. Simplify – divide the power by index (where possible)
Ex. 7:
3
b17
1. Find the largest perfect power, depending on the index, that can be factored
out. (Must be divisible by the index)
2. Re-write using the new powers
3. Simplify – divide the power by index (where possible)
Ex. 8:
11
Ex. 9: a 20a
x9 y 6
Ex. 11:  3 4 x 3 y 9 z 12
Ex. 12:
3
Ex. 10: x
 81ab 4
3
32x10
Ex. 13: 3 yz 108 x 3 y 5 z 10
Homework: Copy each problem into your notebook and show all work there.
Express each in simplest radical form.
1.
100x 4
5.  2 108 x10 y 7
2.
162x 7
6.  2 3 192a 3b 5
8. √9𝑎2 + 9𝑏 2 (be careful, tough one!)
3.
3
3
 8y 5
7. √24𝑎
4. 3 4 80 x 9
3 4 5
3
8. 2  16a b c