Simplifying Radicals

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Simplifying Radicals

• Lesson 13.2

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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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An expression with radicals is in simplest form
if the following are true

1. No radicands (expressions under radical signs)
   have perfect square factors other than 1.
2. No radicands contain fractions.
3. No radicals appear in the denominator of a
   fraction.

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Product Property

• The square root of a product equals the product
  of the square root of the factors.
• For example

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Quotient Property

• The square root of a quotient equals the quotient
  of the square root of the numerator and
  denominator.
• For example

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If the radical in the denominator is not the
square root of a perfect square, then a different
strategy is required.

• Simplify 1 .

To simplify this expression, multiply the
numerator and denominator by v2.
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Practice

5. .

3 v12 v12 v12
3 2v3 12
v3 2
v1 v8 v8 v8
v8 8
2v2 v2 24 4
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Find the area of a rectangle

• Find the area of a rectangle whose width is v2
  inches and whose length is v30 inches. Give the
  result in exact form (simplified) and in decimal
  form.

Area Length Width v30 v2
v60 v4 v15 2v15 about 7.746
square inches.
v2 in.
v30 in.