Objectives The student will be able to:

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ObjectivesThe student will be able to
1. simplify square roots, and 2. simplify
radical expressions. SOL A.3
Designed by Skip Tyler, Varina High School
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If x2 y then x is a square root of y.
In the expression , is the radical
sign and64 is the radicand.

• 1. Find the square root
• 8
• 2. Find the square root
• -0.2

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3. Find the square root

• 11, -11
• 4. Find the square root
• 21
• 5. Find the square root

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6. Use a calculator to find each square root.
Round the decimal answer to the nearest
hundredth.

• 6.82, -6.82

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What numbers are perfect squares?

• 1 1 1
• 2 2 4
• 3 3 9
• 4 4 16
• 5 5 25
• 6 6 36
• 49, 64, 81, 100, 121, 144, ...

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1. Simplify

• Find a perfect square that goes into 147.

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2. Simplify

• Find a perfect square that goes into 605.

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Simplify

1. .
2. .
3. .
4. .

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How do you simplify variables in the radical?

• Look at these examples and try to find the
  pattern

What is the answer to ?
As a general rule, divide the exponent by two.
The remainder stays in the radical.
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4. Simplify

• Find a perfect square that goes into 49.

5. Simplify
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Simplify

1. 3x6
2. 3x18
3. 9x6
4. 9x18

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6. Simplify

• Multiply the radicals.

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7. Simplify

• Multiply the coefficients and radicals.

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Simplify

1. .
2. .
3. .
4. .

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How do you know when a radical problem is done?

1. No radicals can be simplified.Example
2. There are no fractions in the radical.Example
3. There are no radicals in the denominator.Example

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8. Simplify.

• Divide the radicals.

Uh oh There is a radical in the denominator!
Whew! It simplified!
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9. Simplify
Uh oh Another radical in the denominator!
Whew! It simplified again! I hope they all are
like this!
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10. Simplify
Uh oh There is a fraction in the radical!
Since the fraction doesnt reduce, split the
radical up.
How do I get rid of the radical in the
denominator?
Multiply by the fancy one to make the
denominator a perfect square!