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Simplifying Radicals (Pre-Requisite for section 7.2)

Simplifying Radicals (Pre-Requisite for section 7.2)

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Simplifying Radicals (Pre-Requisite for section 7.2)

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  1. Simplifying Radicals(Pre-Requisite for section 7.2) Objective: To write a radical in its simplest form using properties of radicals

  2. Notes: A square root radical is in simplest form when: • There is no perfect square factor under the radical except for the number 1 • There is no fraction under the radical

  3. We use the properties of radicals to simplify: • Multiplication Property: • Division Property:

  4. Let’s make a list of the perfect squares for 1 through 12 to help us: The relationship between the numbers in the table is IF THEN

  5. List a factor pair of the following numbers that contain a perfect square: • 12 • 75 • 32 • 98 Now simplify the following:

  6. Simplify:

  7. Simplify:

  8. Why are we doing this??? When you take the square root of a non-perfect square, it is an irrational #, meaning the # is non-repeating and non-terminating. When you round the value you get in your calculator, it’s not exact. Leaving it in simplest radical form is the EXACT value.

  9. Rationalizing the denominator: