Algebra 1 Notes SOL A.3 Radicals
Mr. Hannam
Name: _______________________________________ Date: _______________ Block: ________
Radical Review

A perfect square is ________________________________________________________________.

The first 12 perfect squares are: ___________________________________________________.

A square root of a number is ______________________________________________________.

Find:

Estimating square roots: find the closest perfect square
36
49
33
144
o Estimate to the nearest whole number:

The

By default, take the square root. Example:
35
55
99
symbol is called a radical. The number inside is the radicand.
42 4= 2
Simplifying Radicals
A radical expression is in simplest form if:

No perfect squares other than 1 are in the radicand

No fractions are in the radicand

No radicals appear in the denominator of a fraction
We use the Product Property of Radicals and Quotient Property of Radicals to simplify:
Product Property of Radicals
The square root of a product equals
the product of the square roots of the
factors:
ab  a  b
Example: 4  9  4  9

Quotient Property of Radicals
The square root of a quotient equals the
quotient of the square roots of the
a
a
numerator and denominator:

b
b
Example:
Method 1: Prime Numbers

Find prime factors of the radicand

Remember that
Example: Reduce
36
36

4
4
a • a  a for any number a
24
1) Find prime factors: 24  2  2  2  3
2) Therefore:
24  2  2  2  3 Look for pairs of the same number!
2 2 23  2 2  23  2 23  2 6
3) Reduced:
24  2 6
You try: Simplify
32 using prime factor method
Algebra 1 Notes SOL A.3 Radicals

Mr. Hannam Page 2
Method 2: Product of Perfect Squares

Re-write the radicand as the product of perfect squares, and then take the roots of
those perfect squares.
1) Know your perfect squares (it is helpful to write a list: _____________________________)
2) Find the biggest perfect square that is a factor of that number, and write the
radicand as a product
3) Take the square root of the perfect square, leaving the other factor inside the radical
Example: Reduce


The biggest perfect square that is a factor of 24 is 4
Rewrite: 24  4 6

Use Product Property and take square root:
You try: Simplify


24
24  4 6  4  6  2 6
32 using the product of perfect square method
If the radicand is a fraction, “split up” the radical into the numerator and
denominator, and then simplify
13
Example: Simplify
100
13
13
o “Split up”:

100
100
o Simplify numerator and denominator. Put in simplest form.
18
o You Try: Simplify
4
You try: Simplify the radical expressions – use both methods!
a)
81
b)
48
c)
75
d)
20
9
Rationalizing Denominators

The process of eliminating a radical in a denominator is called rationalizing the
denominator.

Remember that
a) Example:
a • a  a for any number a
5
5
7 5 7



7
7
7
7
b) You try:
2 5
(Hint: simplify all radicals first!)
24
You try: Simplify the radical expressions…
a)
20
b)
72
c)
28
d)
9
16
e)
1
2
f)
6
12