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- Algebra 1 Notes Name: ________________________ Period: _______Date: ____________ Questions/Main Ideas: TOPIC: Square roots and Cube roots What is a square? CLOs: Identify squares and cubes. Distinguish between a perfect squares and cubes and radicals. Simplify radicals by factorizing numbers and variables. When we multiply an integer by itself we call the product the square of the number. Why might this be? What is a cube? If 4 x 4 = 16, then we can say the square of 4 is 16 and it is written as ______. What is an integer? Draw a picture to illustrate why we call these products squares. Draw a number line that includes negative numbers. Listening: You'll hear different words used when people talk about squares. Square of a number : A squared number: 3 squared: you’ll hear What's the square of 9? Perfect square: illustrate Square Roots written as You can think of finding square roots as the inverse of finding squares. You find the square root of a number (let's call it number A) by finding the number that, when multiplied by itself produces number A. The examples below show this: Think of these examples: 4 x 4 = 16 and - 4 x - 4 = 16. talk about Positive numbers have two square roots; a positive (called the principal square root) and a negative. The symbol find-finding n means give the principal square root. Try these: 25 16 100 What happens if the negative is inside the radical? Answer: ______________________________________________ inside 9 let’s do some thinking Let’s do some thinking. Suppose you were asked to find lie between 40 ? Is the answer an integer? ____________________ What two squares does 40 lie between? ______________________________ So, the square root of 40 is between which two numbers? _____________________ closest to Which number do you think it would be closest to and why? ____________________ Use you calculator to find 40 and round your answer to the nearest tenth. Draw a square. Plot this on a number line. Draw a cube. Try these: Find the root. Give you answers to the nearest tenth and graph on a number line. 15 What is DIMENSION? How many dimensions does a square have? 51 8 When we multiply an integer by itself then by itself again, we call the product the cube of the number. Why might this be? How many dimensions does a cube have? If 2 x 2 x 2 = 8, then we can say the cube of 2 is 8 and it is written as ______. Draw a picture to illustrate why we call these products cubes. Try these: 3 3 125 27 3 8 This time, we can have the negative under the radical. Can you simplify that one? Can you estimate line? 3 50 to the nearest tenth and plot your answer on a number Identify the following parts of a radical: n a Simplifying Radicals Let’s learn how to simplify radicals. That is, put the radical in simplest form. Examples: 1) 24 2) 12 3) 72 4) 3 72 Now let us simplify radicals that contain variables in the radicand. Examples: 64 y 6 1) 2) 3 24x 6 y 4 z 7 You Try: 3 3) Summary: 125x12 4) 243x15 y 8 z 9