# Product Property of Radicals ```ALGEBRA O.T.Q.
Identify the perfect square in each set.
1. 45, 81, 27, 111
2. 156, 99, 8, 25
3. 256, 84, 12, 1000
4. 35, 216, 196, 72
Find the Prime Factorization of each number.
5. 36
6. 64
7. 196
8. 24
10.2
Simplifying
What will I be able to do?
Simplify radical expressions using the
Product and Quotient Property of Square Roots
When simplifying a radical
expression, find the factors that
are to the nth powers of the
radicand and then use the
Product Property of Radicals.
What is the Product
Product
Property of
For any positive real
numbers a and b, the
square root of ab is
equal to the square root
of a times the square
root of b
=
1.
8
144x y
5
Factor into squares
144 = 12&sup2;
=
2
4 2
2 2
12  (x ) (y )  y
Product Property of Radicals
2
4 2
2 2
12  (x )  (y )  y
4
12x y
2
y
3
2
2) 7 64n  4 8n 
3
Product Property of Radicals
3
2
7  4  64n 8n
Factor into cubes if possible
3
3
28  (4)  (2)  n
3
3
Product Property of Radicals
3
3
3
28  (4)  (2)  n
3
3
28  4 2  n  224n
3
Now, you try
these
examples.
2.
Quotient
For real numbers a and b,
Property of b  0 the square root of
is equal
to the square root
,
of a divided by the
square root of b
=
Simplify the
expression.
6
x

3
y
1)
3
x
x

2
y
y
x3

y y
6
x
3
y
3
Rationalize the denominator
3
x

y y
3
y
x y


y
yy
x
3
y
2
y
When there is a
binomial with a
denominator of
a fraction, you
find the
conjugate and
multiply.
Ex:
5  6  Conjugate:
56
3  2 2  Conjugate: 3  2 2
Simplify:
56
53
Multiply by the conjugate
56
56 53


53
53 53
FOIL numerator and denominator
5  3 5  6 5  18
59
Combine like terms
23  9 5
4
SUMMARY!
CLASSWORK
Pages 631 – 632 #’s 10 – 34 even, 38 – 44 even, 53(a)
HOMEWORK
Pages 633 #’s 58, 59, 62, 73, 78
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