Objective Students will add, subtract, multiply, divide, and simplify radicals.

Warm-up Define what a perfect square is using your own words. List all of the perfect squares that you can remember off the top of your head.

Simplifying Radicals Simplifying radicals is like creating factor trees, but we are looking for perfect square factors. Example: Are there any perfect squares that are factors of 8? What are they? x

Let’s try these together:

Answers to Simplifying Radicals - Question A

Answers to Simplifying Radicals Question B

Answers to Simplifying Radicals Question C = 9, 306 is divisible by 9 too!

Answers to Simplifying Radicals Question D 32

Adding and Subtracting with Radicals Adding and subtracting with radicals is a lot like combining like terms. You can only add or subtract “like” radicals. Example: “Like” radicals: Add the coefficients! Final answer!

Try these on your own!

Question A Add/Subtract Since each term contains radical 2, just combine the coefficients!

Question B Add/Subtract “like” radicals

Question C Add/Subtract Simplify radicals that you can simplify. Combine “like” radicals.

Multiplying with Radicals When multiplying a radical by a radical: –multiply the coefficients –multiply the radicals –then simplify the radical if possible. Example: Final Answer? What property?

Try these :

Question A Multiplication Multiply Simplify Final Answer

Question B Multiplication Method 1 Method 2

Question C Multiplication Distributive Property Multiply and Simplify

Question D Multiplication Which answer did you choose?

Dividing with Radicals

Let’s kick it up a notch… Simplify using radicals.

Question A - Division Simplify the radical. Take the square roots of perfect squares. Divide by 5. This is your final answer!

Question B - Division Choice #1 = 1.08 Choice #2 = Choice #3 =

Question C - Division Simplify each radical. Take square roots. Simplify as a fraction (if possible).

Question D - Division