# Identify Square Numbers

In this worksheet, students find square numbers and apply knowledge of square numbers to solve problems.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Indices and Surds

Curriculum subtopic:   Structure and Calculation, Powers and Roots

Difficulty level:

### QUESTION 1 of 10

A common misconception about square numbers is that they are a number multiplied by itself.

This is not correct!

A square number is the answer to a number multiplied by itself.

For example, 122 = 12 x 12 = 144

12 isn't the square number, 144 is.

The easiest way to solve problems that involve square numbers is just to know them off by heart, at least the first 15 anyway.

The first 15 square numbers are:

 12 1 x 1 1 22 2 x 2 4 32 3 x 3 9 42 4 x 4 16 52 5 x 5 25 62 6 x 6 36 72 7 x 7 49 82 8 x 8 64 92 9 x 9 81 102 10 x 10 100 112 11 x 11 121 122 12 x 12 144 132 13 x 13 169 142 14 x 14 196 152 15 x 15 225

Let's practise using these numbers in calculations now.

Squaring an integer:

e.g. Find the value of 62

6 x 6 = 36

Squaring a decimal:

One thing examiners like to do is to tie in one topic with another.

If you ever see a question involving squaring a decimal without a calculator, it will be based around the square numbers which you would already have knowledge of.

e.g. Find the value of 1.22

This just means we need to find the value of: 1.2 x 1.2

If we look at our table, we can see that:

12 x 12 = 144

So 1.2 x 1.2 = 1.44 when we put out decimal point back in

Great focus!

In this activity, you will find square numbers and apply your knowledge of square numbers to solve problems.

Now let's attack some questions and really consolidate our knowledge.

Complete the sentence below to define a square number

Which of the options in the list are square numbers?

9

60

48

16

90

81

Match each indices below to the square number it creates.

## Column B

52
64
82
1
12
25
112
196
142
121

Work out the answer to the indices below:

0.42

Imagine that the lines below represent your friend's working on an indices calculation.

There is a mistake somewhere in this working.

Can you identify where it occurs?

Choose if each line is correct or not by selecting the relevant box.

 Correct Incorrect 1.32 = 1.3 x 1.3 13 x 13 = 169 1.32 = 16.9

Use the correct symbol ( > or < ) to complete expression below.

 Correct Incorrect 1.32 = 1.3 x 1.3 13 x 13 = 169 1.32 = 16.9

Which of the numbers below is larger?

(-5)2

42

What is the value of the calculation below?

102 - 82 + 22

True or False?

Squaring a number always makes it bigger.

True

False

Which of the options in the list below is the correct answer for 0.04?

1.6

0.16

0.016

0.0016

• Question 1

Complete the sentence below to define a square number

EDDIE SAYS
As we said in the Intro, a square number is the answer to a number when it is multiplied by itself. e.g. 3 x 3 = 9 9 is the square number here, not 3. Remember this essential fact and apply it in the rest of this activity.
• Question 2

Which of the options in the list are square numbers?

9
16
81
EDDIE SAYS
The easiest way to wok this out is to ask yourself: "Is there a number I can multiply by itself to reach this number?" If the answer is no, it isn't a square number. As you become more familiar with square numbers, it is a good idea to try and learn at least the first 15 by heart.
• Question 3

Match each indices below to the square number it creates.

## Column B

52
25
82
64
12
1
112
121
142
196
EDDIE SAYS
You can work these out by multiplying the integer in each indices by itself: e.g. 8 x 8 = 64 However, it is much quicker to commit these to memory so that you can instinctively match common square numbers without having to work them out each time.
• Question 4

Work out the answer to the indices below:

0.42

0.16
EDDIE SAYS
We can see that this question is based around the fact: 4 x 4 = 16 As 0.4 is 10 times smaller than 4 and we are using it twice, our answer must be 100 times smaller than 16: 16 ÷ 100 = 0.16
• Question 5

Imagine that the lines below represent your friend's working on an indices calculation.

There is a mistake somewhere in this working.

Can you identify where it occurs?

Choose if each line is correct or not by selecting the relevant box.

 Correct Incorrect 1.32 = 1.3 x 1.3 13 x 13 = 169 1.32 = 16.9
EDDIE SAYS
Reviewing the working out of others is a really great way to hone your skills. The easy way to spot the error in this one is to estimate the answer you expect before starting: 1.3 rounds down to 1. 1 x 1 = 1 So our answer should be around about 1. Our friend's working has an answer of nearly 17, so something has definitely gone wrong! The first line is correct, as the numbers and decimal points have all been maintained accurately. In the second line, the 1.3s have both been multiplied by 10 which is permitted, so long as both numbers are altered in the same way. In the final line, the answer (169) needs to be divided by 10 x 10 (100), however, it has only been divided by 10. So this is the line where our friend has made an error. If they divided 169 by 100, they would reach the correct answer of 1.69
• Question 6

Use the correct symbol ( > or < ) to complete expression below.

EDDIE SAYS
To solve this, we need to work out the value that 42 represents. 4 x 4 = 16 We now need to decide if 16 is greater than or less than 15, which is easy hopefully!
• Question 7

Which of the numbers below is larger?

(-5)2
EDDIE SAYS
This one can cause problems if you move too quickly. Remember that when you multiply -5 by itself, it ends up becoming a positive overall (as - and - = +). So we need to decide which is larger: (-5)2 = (-5) x (-5) = 25 42 = 4 x 4 = 16
• Question 8

What is the value of the calculation below?

102 - 82 + 22

40
EDDIE SAYS
This question combines the rules of BODMAS / BIDMAS and our knowledge of square numbers. As we've mentioned before, examiners love combining topics in this tricky way! BODMAS tells is to work out the squares first (indices): 100 - 64 + 4 = 40 Well done if you combined those two concepts successfully!
• Question 9

True or False?

Squaring a number always makes it bigger.

False
EDDIE SAYS
This is a tricky one! For most numbers, when you square it, it does indeed get bigger. However, this is not true for numbers between 0 and 1. e.g. 0.5 x 0.5 = 0.25 which is smaller So overall, this statement must be classed as 'False' but it is an interesting fact to remember, so long as you can also recall the circumstances where it does and does not apply.
• Question 10

Which of the options in the list below is the correct answer for 0.04?

0.0016
EDDIE SAYS
We need to think really carefully about this one. We can see that 0.04 x 0.04 has 4 digits in total after the decimal places. Therefore, our answer must have the same. 4 x 4 = 16 so 0.04 x 0.04 = 0.0016 Great work, you've completed another activity! You may want to review BODMAS / BIDMAS or any of the other concepts we combined with square numbers in this activity.
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