Simplifying Radicals(Pre-Requisite for section 7.2) Objective: To write a radical in its simplest form using properties of radicals
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
We use the properties of radicals to simplify: • Multiplication Property: • Division Property:
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
List a factor pair of the following numbers that contain a perfect square: • 12 • 75 • 32 • 98 Now simplify the following:
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.