Simplifying Square Roots

1
Simplifying Square Roots

• Date ___________

2
Objective - To simplify rational and irrational
square roots.
Reals
Rationals
Irrationals
3
Recognizing Rational Roots
Rational Roots
Perfect Squares
4
Identify each root as rational or irrational.
rational
1)
6)
rational
2)
7)
irrational
rational
3)
8)
irrational
rational
4)
9)
rational
irrational
Neither (not a Real number)
5)
10)
irrational
5
Between what two whole numbers does the
irrational root lie?
1)
3)
2)
4)
6
Evaluate. Round to the nearest hundredth
when necessary.
1)
4)
2)
5)
3)
6)
7
Evaluate when a 2, b 3, and c -2. Round
to nearest hundredth when necessary.
1)
2)
8
Evaluate when a 2, b 3, and c -2. Round
to nearest hundredth when necessary.
3)
4)
9
Objective - To simplify irrational roots.
Example
Check using a calculator!
10
Simplify.
To simplify the number must have a perfect square
factor.
No perfect square factors
Cant be simplified
List the perfect square factors from 1 to 300.
11
Simplify each irrational root.
1)
4)
2)
5)
3)
6)
12
Simplify.
Perfect square
13
Simplify each irrational root.
1)
4)
Already Simplified
2)
5)
3)
6)
14
Simplify each irrational root.
7)
10)
8)
11)
9)
12)
Already Simplified
Not a Real Number
15
Objective - To simplify radical expressions
involving addition, subtraction, multiplication,
and division.
16
Simplify.
1)
3)
2)
4)
17
Three Rules for Simplifying Radical Expressions
1) Leave no perfect square factor in a radical.
2) Leave no fractions or decimals in a radical.
3) Leave no radicals in a denominator.
18
Simplify.
1)
4)
2)
5)
3)
6)
19
Simplify.
1)
3)
2)
4)
20
Simplify.
1)
3)
2)
4)
21
Simplify.
1)
2)
22
Simplify.
1)
3)
2)
4)
23
Simplifying a Radical Expression Using a Conjugate
24
State the conjugate of the radical expression.
Radical Expression
Conjugate
25
Simplify.
1)
2)
26
Objective- To simplify square roots involving
variables.
when x 3
when x -3
when x -3
27
Follow the Pattern!
28
Simplify.
29
Simplify.
1)
4)
2)
5)
3)
6)
30
Simplify.
1)
2)
31
Simplify.
1)
3)
2)
4)
32
Simplify.
5)
7)
6)
8)