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, 42 = 16 √16 = √4 x 4 = √42 = 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 = √42 = 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

52 = 5 x 5 = 25Therefore, 5 is the square root of 25. b) 15

152 = 15 x 15 = 225Therefore, 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 = √82 = 8 8 x 8 = 64,

therefore 8 is the square root of 64

b) 36√36 = √6 x 6 = √62 = 6

c) 81 √81 = √9 x 9 = √92 = 9

So…the side length of a square represents the square root of the number represented by the area of the square.

6 cm

6 cm

Area is 36 cm2

-36 is a square number

-6 is the square root of 36

A = 36cm2

Complete the worksheet handed out.

P. 15-16 #5, 6, 7, 13, 14, 16 For #16, use the Step-by-Step sheet

provided.