Radical Unit Simplifying Radicals

Medina 1

Simplifying Radicals

Medina 2

Rule 1:

There are NO perfect squares underneath the radical symbol.

There are NO fractions underneath the radical symbol.  

Rule 2:

Rule 3:

There are NO radicals in the denominator.  

Rule 4:

There are NO negatives underneath a square root.  

Simplifying Radicals

1• 8

8

1st Method : Ask yourself, what are the factors of 8? 

2• 4

Think of biggest perfect square that’s a factor of 8:4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, ..., 625 2• 4

2 2

Any number(s) that does not have a square root stays in the radical.

Simplifying Radicals

1• 18

18

1st Method : Ask yourself, what are the factors of 18? 

2• 9

Think of biggest perfect square that’s a factor of 18:4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, ..., 625 2• 9

3 2

3• 6Or when in doubt, prime factor out.

18 2 3 3

Simplifying Radicals

1• 54

54

1st Method :Ask yourself, what are the factors of 54? 

2• 27

Think of biggest perfect square that’s a factor of 54:4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, ..., 625

6• 9

3 6

3• 186• 9

Or when in doubt, prime factor out.

54 2 3 3 3

Simplifying Radicals

Medina 6

5

9

5

3

Simplifying Radicals

Medina 7

3

4

3

2

Simplifying Radicals

Medina 8

8

9

8

3

2• 4

32 2

3

Solving Radical Equations

Medina 9

x

2 12xTo Solve:

Means there are 2 answers 2 12x

x 3 4

2 3