1. Square Roots and Radicals Square Root of a Number:
Radical Symbol:
Radicand:
Special Cases:
Perfect Squares: MEMORIZE!!
12= 112=
22= 122=
32= 132=
42= 142=
52= 152=
62= 162=
72= 172=
82= 182=
92= 192=
102= 202=
If b2 = a, then b is a square root of a
The number inside the radical symbol
The (positive) square root of 16.
The negative square root of 16.
This is read “plus or minus the square root of 16”.
Zero has only one square root.
Negative numbers have
NO REAL SQUARE ROOTS.
A number times itself will NEVER be negative!

2. Find the two closest perfect squares (greater than and less than)
Approximate the value of a non-perfect square root:
Steps: 1) 2) 3)
Find the two closest perfect squares (greater than and less than)
See where your number fits in
Make a decimal approximation (nearest tenth)

3. The radicand can have no perfect square factors (except 1)
Simplifying square root (or radical) expressions:
Product Property Quotient Property
* LOOK FOR PERFECT SQUARE FACTORS
Examples:
The radicand can have no perfect square factors (except 1)
There can be no radical in the denominator
to remove from the radicand.
If you don’t see any right away, factor the radicand completely and pull out pairs. Leave “singles” in the radical.

4. Simplifying square root (or radical) expressions cont.