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

ALGEBRA O.T.Q.ALGEBRA O.T.Q.

10.2 Simplifying

What will I be able to do?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 Property of Radicals???

Product Property of Radicals

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. 144x8 y5

122 (x4 )2 (y2 )2 y

Factor into squares

122 (x4 )2 (y2 )2 yProduct Property of Radicals

12x4 y2 y

144 = 12²

=

2) 7 64n23 4 8n3 7 4 64n2 8n3

Product Property of Radicals

28 (4)3 (2)3 n33

Factor into cubes if possible

28 42 n 224n

28 (4)33 (2)33 n33

Product Property of Radicals

Now, you try these examples.

2.

Quotient Property of Radicals

0,

For real numbers a and b, b the square root of is equal to the square root of a divided by the square root of b

=

Simplify the expression.

1) x6

y3

x6

y3

x3

y2

x3

y

x3

y y

x3

y y

y

y

Rationalize the denominator

x3 y

yy

x3 y

y2

When there is a binomial with a radical in the 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

5 6

5 3

5 6

5 3

5 3

5 3

Multiply by the conjugate

5 3 5 6 5 18

5 9

FOIL numerator and denominator

Combine like terms

23 9 5

4

SUMMARY!SUMMARY!

CLASSWORKCLASSWORK

HOMEWORKHOMEWORK

Pages 631 – 632 #’s 10 – 34 even, 38 – 44 even, 53(a)

Pages 633 #’s 58, 59, 62, 73, 78