Identify the perfect square in each set. 1. 45, 81, 27, 111 2. 156, 99, 8, 25 3. 256, 84, 12, 10004....
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Transcript of Identify the perfect square in each set. 1. 45, 81, 27, 111 2. 156, 99, 8, 25 3. 256, 84, 12, 10004....
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.
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
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