Chapter 1: Square Roots and the Pythagorean Theorem 1.2 Square Roots.

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Presentation transcript:

Chapter 1: Square Roots and the Pythagorean Theorem 1.2 Square Roots

Refresher from last class  square number – the product of a number multiplied by itself; for example, 25 is the square of 5.  See you if you can name the first 10 square numbers, starting at zero. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100  When we multiply a number by itself, we square that number.  Highlight every square number on your multiplication table – what do you notice?

 If you highlight each square number you will see a pattern forming from the top left-hand corner, to the bottom right-hand corner.

 Squaring and taking the square root are the inverse operations. That is, they undo each other. √ is the square root symbol  4 x 4 = 16 so, 4 2 = 16  √16 = √4 x 4 = √4 2 = 4  Think of inverse operations as turning a light switch on and off – they undo each other.

 **Since squaring and finding the square root are inverse operations, if you see a number that is both squared and under a square root sign, they cancel each other out.**  Example: √16 = √4 x 4 = √4 2 = 4 Here you see the 4 is both squared and under the square root sign. They cancel each other out and you are left with just 4.

 Find the square of each number: a) = 5 x 5 = 25 Therefore, 5 is the square root of 25. b) = 15 x 15 = 225 Therefore, 15 is the square root of 225.

 Find the square root of the following: (in other words, find the number that, when multiplied by itself, gives the following…) a) 64 √64 = √8 x 8 = √8 2 = 88 x 8 = 64, therefore 8 is the square root of 64 b)36 √36 = √6 x 6 = √6 2 = 6 c)81 √81 = √9 x 9 = √9 2 = 9

 So…the side length of a square represents the square root of the number represented by the area of the square. 6 cm Area is 36 cm is a square number -6 is the square root of 36 A = 36cm 2

 Complete the worksheet handed out.  P #5, 6, 7, 13, 14, 16  For #16, use the Step-by-Step sheet provided.