Page 17 - Mathematics Coursebook

1.6 Squares and square roots

1.6 Squares and square roots

1 × 1 = 1 2 × 2 = 4 3 × 3 = 9 4 × 4 = 16 5 × 5 = 25

!e numbers 1, 4, 9, 16, 25, 36, … are called square numbers.
Look at this pattern.

1 4 9 16

You can see why they are called square numbers.

!e next picture would have 5 rows of 5 symbols, totalling 25

altogether, so the "&h square number is 25.

!e square of 5 is 25 and the square of 7 is 49.

2
You can write that as 5² = 25 and 7² = 49. Be careful: 3 means 3 × 3, not 3 × 2.
Read this as ‘5 squared is 25’ and ‘7 squared is 49’.
You can also say that the square root of 25 is 5 and the Adding and subtracting, and multiplying
square root of 49 is 7. and dividing, are pairs of inverse

!e symbol for square root is . operations. One is the ‘opposite’ of the
25 = 5 and 49 = 7 other.
Squaring and fi nding the square root are
25 = 5 means 5 = 25 also inverse operations.
2

) Exercise 1.6

1 Write down the first ten square numbers.

2 Find 15² and 20².

3 List all the square numbers in each range.
a 100 to 200 b 200 to 300 c 300 to 400

4 Find the missing number in each case.
a 3² + 4² = ² b 8² + 6² = ²
c 12² + 5² = ² d 8² + 15² = ²

5 Find two square numbers that add up to 20².
6 The numbers in the box are square numbers.
a How many factors does each of these numbers have? 16 25 36 49 81 100
b Is it true that a square number always has an
odd number of factors? Give a reason for your answer.
7 Find:
a the 20th square number b the 30th square number. c the 50th square number.

16 1 Integers