Operations with Radicals

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Operations with Radicals

• Lesson 13.3

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Learning Goal 1 (HS.N-RN.B3 and
HS.A-SSE.A.1) The student will be able to use
properties of rational and irrational numbers to
write, simplify, and interpret expressions based
on contextual situations.
4 3 2 1 0
In addition to level 3.0 and above and beyond what was taught in class,  the student may         Make connection with other concepts in math         Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the  sums and products of rational and irrational numbers -interpret expressions within the context of a problem The student will be able to use properties of rational and irrational numbers to write and simplify  expressions based on contextual situations. -identify parts of an expression  as related to the context and to each part With help from the teacher, the student has partial success with real number expressions. Even with help, the student has no success with real number expressions.
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Like Radicals

• Two radical expressions are like radicals if they
  have the same radicand.
• For instance, v2 and 3v2 are like radicals.
• To add or subtract like radicals, add or subtract
  their coefficients.
• v2 3v2 (1 3)v2 4v2
• v2 - 3v2 (1 3)v2 -2v2

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Practice

1. 2v3 v2 - 4v3
2. -2v3 v2 Add like radicals.
3. 3v2 - v8
4. 3v2 - v4 v2 Product Property
5. 3v2 - 2v2 Subtract like radicals.
6. v2

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Multiplying Radicals

• 3v2(v2 4v6)
• (3v2)(v2) (3v2)(4v6) Distributive Property
• 3(v2 v2) (34)(v2 v6) Regroup
• 3v4 12v12 Product Property
• 3v4 12v43 Perfect square factor
• 3(2) 12(2)v3 Simplify
• 6 24v3 Simplest form

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Practice simplify the radical expressions.

1. 4v3 - 5v3
2. -6v12 v75

-v3
-6v43 v253 -12v3 5v3 -7v3
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Multiply and Simplify

1. 2v3(v2 5v6)
2. 3v8(v3 5)

2v6 10v18 2v6 10v92 2v6 30v2
3v24 - 15v8 3v(46) - 15v(42) (32)v6 -
152v2 6v6 - 30v2