Extending Your Knowledge

Grade 8 Mathematics Mr. J. Lingley

P2 - Predicting PatternsPerfect Squares

1

4

9

16

25

36

3

5

7

9*

11

Perfect Squares

49

64

81

100

13

17

19

P2 - Predicting Patterns3 5 7 11 13 17 19

What do all of these have in common?

2

P2 - Predicting Patterns3 5 7 11 13 17 19

What do all of these have in common?

They are prime numbers.

2

List of Square Numbers

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225

256 289 324 361 400 441 484 529 576 625 676 729 784 841 900

961 1024 1089 1156 1225 1296 1369 1444 1521 1600 1681 1764 1849 1936 2025

2116 2209 2304 2401 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 3600

Looking at the ones position, do you see any patterns?

List of Square Numbers

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225

256 289 324 361 400 441 484 529 576 625 676 729 784 841 900

961 1024 1089 1156 1225 1296 1369 1444 1521 1600 1681 1764 1849 1936 2025

2116 2209 2304 2401 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 3600

Looking at the ones position, do you see any patterns?

All square numbers end in 1, 4, 9, 6, 5, or 00

Prime Factorization A long word, for a very long (but geeky) process.

Say we want to find the square root of a larger square number like 441.

Might seem impossible, but all we need to remember are a couple of math strategies.

Prime Factorization A long word, for a very long (but geeky) process.

Say we want to find the square root of a larger square number like 784.

√784 What do we notice about this number? Let’s think about our divisibility rules...

Prime Factorization A long word, for a very long (but geeky) process.

Say we want to find the square root of a larger square number like 784.

√784 What do we notice about this number? Let’s think about our divisibility rules...

Since this is an even number, it must be divisible by 2.

Prime Factorization A long word, for a very long (but geeky) process.

Say we want to find the square root of a larger square number like 784.

√784 What do we notice about this number? Let’s think about our divisibility rules...

Since this is an even number, it must be divisible by 2.

We now use the smallest prime number (2) to simplify 784.

√784√ 2 x 392

√ 2 x 2 x 196√ 2 x 2 x 2 x 98

√ 2 x 2 x 2 x 2 x 49

√ 2 x 2 x 2 x 2 x 7 x 7

( 2 x 2 x 7 ) x ( 2 x 2 x 7 )

√ ( 28 ) x ( 28 ) = 28

Your Turn1. Using prime factorization, find the square roots of:

√225 √484 √324

2. Which of the following numbers is a square number?How do you know?

√_ _ 8 √_ _ 6

√_ _ _ _ 9 √_ _ _ _ _ 2