Activator Using the cubes in front of you build the following square shapes: 2 by 2, 3 by 3, and 4 by 4 How many blocks were in each square shape? What do you notice between the number of blocks in the shape and the way you were asked to build them?

Square Roots What do you think of when you hear the word square? Now get shapes out of your head and think numbers.

Activator Any # times itself is called what? Any # times itself 3 times is called what?

Square Roots Squares Cubes

Squares and Square Roots This lesson is divided into two parts, the numbers and their roots. A whole number can be referred to as a square: Meaning that you can multiply the same number by itself to achieve the whole number: Example: 4 is a square, because 2 x 2 = 4

Squares and Square Roots The number that you multiply by itself to get the whole number is the square root. So 2 is the square root of 4. Not every whole number has a perfect square root, meaning that not every number has a whole number that can be multiplied by itself to get the square. Example: 2 does not have a perfect square root. 1. 4142135623… x 1.4142135623…= 2

Squares and Square Roots The numbers that do not have perfect square roots have irrational square roots. √ this symbol is called a radical: The number under the radical is called the radicand. √7 so 7 is the radicand and √ is the radical.

Square Root √8 Radicand: # under the radical Radical or root symbol

Practice √36 √49 √144 √169

Cube Root This is the index #. It tells how many times you would multiply the root by to get the radicand √8 Radicand: # under the radical 3 Radical or root symbol

Squares and Square Roots √ this is the symbol for root: When you see this before a number: √4 it is asking for the number that can be multiplied by itself to form the number inside. The √ usually does not have an index of 2 when asking for the square root, but with other roots you will see a tiny number above the radical to indicate what type of root you are looking for. Examples: √8 or √8 both mean square root, but √9 means the cube root or what times itself 3 times will equal 9 2 3

Practice 3√27 3√8 3√64 3√1000

Perfect Squares and Square Roots

Approximating Square and Cube Roots To approximate a root find the two perfect roots the number would fall between: Ex: √74 is between the √64 and √81 Which is closer to √74? What is the square root?

Assessment Prompt What is the difference between a square root and a cube root? What are perfect squares and cubes? How many square roots does every number have? What is the positive square root called?

Recognizing when a square root is irrational. Activator: What are irrational numbers? Write the prime factorization of 84 (use a factor tree)

Factor Trees √36 6 (Perfect square) 3 12

Factor Trees √48 2 * 2 √3 = 4√3 (Not Perfect) 6 8 3 2 4 2 2 2

Factor Trees √64 8 (Perfect square) 8 8

Practice: √25 √49 √28

Cube Roots 3 √27 What number can you multiply itself 3 times will equal 27 27 9 3 3 3

Practice 3 √64 √8 √120 3 3

Radical Race Start with the square root of 9 Next person add 13 to the answer above Next person find the square root to the answer of #2 Next person multiply the answer to #3 by 16 Next person find the square root to #4 answer Hold up your answer when your group is finished