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Benchmark:H.1.1.a. Extend the properties of exponents to rational exponents.
H.1.1.a.ii. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Objectives: find all the prime factors of a number simplify radical expressions
Radicals
Because = 4 : 2 is a square root of 4
In the expression , the is the radical sign and 64 is the radicand.
22
Example1
Find the square root:
Practice1
Find the square root:
0.2
Perfect Squares
List some perfect squares.
1• 1= ____ 2•2 = ____ 3•3 = ____
4•4 = _____ 5•5 = _____ 6•6 = ____
7•7 = ____ 8•8 = _____ 9•9 = _____
10•10 = ______
1 4 9
16 25 36
49 64 81
100
The FANCY way to simplify a radical expression
Simplify :
Ugly Answer: ____________
12.1244
The FANCY way to simplify a radical expression
Simplify :
Step 1: Find a perfect square that goes into 147.
The FANCY way to simplify a radical expression
Simplify :
Step 2: Split up the radical and simplify.
The EASY way to simplify a radical expression
Factoring is a way to find ALL the prime numbers that go into a number.
A prime number can only be divided by 1 and itself.
Example 2
Find all the prime factors of 300.
300
1502
275
515
53
Practice 2
Find all the prime factors of 126.
126
632
321
37
The EASY way to simplify a radical expression
When simplifying a square root, the first step is to factor the number.
Only take 1 number from each pair outside of the radical.
Example 3: Use whiteboard to factor
Simplify the following expression:
605
1215
1111
Example 3
Simplify the following expression:
11
Example 3
Simplify the following expression:
DOUBLE CHECK!!
24.596724.5967
Practice 3
Simplify the following expression:
72
362
218
29
33
Practice 3
Simplify the following expression:
2
Practice 3
Simplify the following expression:
DOUBLE CHECK!!
8.485288.48528
Example 4
Simplify the following expression:
75
155
35
Simplify the following expression:
Example 4
Practice 4
Simplify the following expression:
90
452
59
33
Simplify the following expression:
Practice 4
Example 5
Simplify the following expression:
49
77
4 22 49a b
Simplify the following expression:
2 7 7 aaaabb
Example 5
2214a b
4 22 49a b
Practice 5
Simplify the following expression:
8
42
22
Practice 5
Simplify the following expression:
46 2x x
2x
Example 6
The formula can be used to find the size of a square sector where a is the area of the square and s is the length of a side. What is the length of the side of a square with an area of 729 sq. miles?729 = a or s?
27miles
Whiteboards!!!
Find the square root:
26
36
6
Find the square root:
29
81
9
Find the square root:
27
49
7
Draw a factor tree for: 50
50
105
25
Simplify the following expression:
5 5 2
50
5 2
5
Draw a factor tree for: 63
63
97
33
Simplify the following expression:
3 3 7
63
3 7
3
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