Transcript Prime Factorization and GCF

Simplifying Radicals
NF.4.AC.2: Simplify, add, subtract and multiply
radical expressions
Students will learn to simplify radicals and to
multiply and/or divide radical expressions
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Algebraic Connections
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What is a factor?
• We say that we have factored 12 when we
express 12 as the product of two or more
integers (for example 12 = 3 • 4) We call
3 and 4 factors of 12.
• Let’s name some factors of 24:
2 and 12
3 and 8
6 and 4
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Algebraic Connections
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What is a prime number?
• A prime number is a number whose only factors
are itself and 1.
• 2, 3, 5, 7, etc. are examples of prime numbers.
• Let’s see if we can name 4 more prime numbers:
11
13
17
19
• All numbers that are not prime, we call composite
numbers.
• They are made up of prime factors. To find all
the prime factors, we will use prime factorization.
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Algebraic Connections
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Prime Factorization
• To find the prime factorization, we will learn
to use a factor tree.
• We start our factor tree with 24.
24
Then we think of 2 factors of 24.
• Now 2 factors of 12
2
12
• Now 2 factors of 6
• Why don’t we find factors of 2 or 3?
2
6
They are prime numbers.
So, the prime factorization of 24 is
2
3
3
2∙2∙2∙3=2 ∙3
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Algebraic Connections
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What is a radical?
• The square root of a number is written using the
symbol
and is called a radical.
• The number written inside this symbol is called
the radicand.
• We need to simplify any radical that has a
perfect square (a number with a whole number
square root) as a factor of the radicand.
• We use prime factorization to help with
simplifying the radical.
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Algebraic Connections
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Simplifying Radicals
The steps for simplifying a radical are as
follows:
1. Use a factor tree to find the prime
factorization.
2. Circle any pair of numbers.
3. Put one of each of the pairs of circled
numbers outside the radical sign.
4. All numbers not circled go inside the radical
sign.
5. Simplify the outside and inside of the radical.
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Algebraic Connections
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Simplifying a Radical
To simplify this radical
45
1. Find the prime factorization
of 45.
2. Circle any pair of identical
numbers.
3. The circled number goes
outside the radical sign.
4. The uncircled number goes
inside the radical sign.
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Algebraic Connections
45
5
9
3
3
3 5
7
Simplifying a Radical
To simplify this radical
90
1. Find the prime factorization
of 90.
90
2.Circle any pair of identical
numbers.
3.The circled number goes
outside the radical sign.
4.The uncircled numbers go
inside the radical sign.
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Algebraic Connections
9
3
10
3 2
5
3 2·5
3 10
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Simplify These Radicals
1.
12
2 3
2.
75
5 3
3. 24
2 6
18
3 2
4.
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Algebraic Connections
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