Objective

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Objective

• SWBAT review simplifying radical expressions,
  solving radical equations, applying the
  Pythagorean theorem, and applying the distance
  and midpoint formula.

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Section 11.2 Simplify Radical Expressions

• A radical expression is in simplest form if the
  following conditions are true

• No perfect square factors other than
• 1 are in the radicand.

-No fractions are in the radicand.

• No radicals appear in the
• denominator of a fraction.

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Product Property of Radicals

• The square root of a product equals the product
  of the square roots of the factors.

Quotient Property of Radicals

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

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Rationalizing the Denominator

• Whenever there is a radical (that is not a
  perfect square) in the denominator, the radical
  must be eliminated by rationalizing the
  denominator.

Need to rationalize the denominator
Multiply by 1
Product property of radicals
Simplify
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Adding and Subtract Radicals

• You can add and subtract radicals that have the
  same radicands.

Think of as combining like terms
Look for common radicands
Simplify
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Multiplying Radical Expressions

• You can multiply radical expressions the same way
  you multiplied monomials and binomials using the
  distributive property and FOIL.

simplify combine like terms
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Section 11.3 Solve Radical Equations

• An equation that contains a radical expression
  with a variable in the radicand is called a
  radical equation.
• To solve a radical equation, you need to ISOLATE
  the radical on one side and then square both
  sides of the equation.

If
then
If
then
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Section 11.4The Pythagorean Theorem

• For any RIGHT TRIANGLE, the sum of the squares of
  the lengths of the legs, a and b, equals the
  square of the length of the hypotenuse, c.

c
a
b
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The Right Triangle
hypotenuse (always across from the right
angle and always the longest side ).
c
right angle (90)
a
b
legs
10

• Your cat is at the top of a 15 foot tree. The
  bottom of the ladder that you will use will be
  placed 9 feet from the base of the tree. Can you
  reach the cat if the ladder is 20 feet in length?
  

15 feet
9 feet
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Section 11.5 The Distance and Midpoint Formulas

• Distance Formula

y
To find the distance between two points
x
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Section 11.5 The Distance and Midpoint Formulas
y

• Midpoint Formula

The midpoint (middle point) between two points
can be found by
x
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Chapter 8 Final Review
7)
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8)
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Chapter 9 Final Review
7)
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8)
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Do Now 6/14/10

• Take out HW from Friday.
• Review worksheets 9-10. We will correct after
  the review.
• Copy HW in your planner.
• Chapter 12 Test tomorrow.
• Review worksheets Chapter 11 12 due Wednesday.
• In your notebook, write and simplify a rational
  expression for the ratio of the perimeter of the
  given figure to the area. (Area of a triangle ½
  the base times the height.)

(2x 3) (2x 2) (2x 1)
2x 1
2x 3
½ (2x)(2x 2)
2x
6x 6
6(x 1)
3
2x 2
2x² 2x
2x(x 1)
x