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Calculate Square Roots (Without a Calculator)

In this worksheet, students will find square roots of whole numbers and decimals without using a calculator.

'Calculate Square Roots (Without a Calculator)' worksheet

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:  

Worksheet Overview

QUESTION 1 of 10

Square roots are a topic where mistakes can be easily made.

To try and define it in simple words lets say to ourselves: 

"The square root of a number is what you would multiply by itself to reach this number."

 

 

e.g. If we are trying to find √81...

We should ask ourselves first:

"What do I multiply by itself to reach 81?"

The answer is 9.

So √81 = 9

 

 

Square roots of decimals

If you are ever asked to find the square root of a decimal without a calculator, it is much simpler to use a square number that you already know.

 

e.g. Find √1.21

 

We need to look for a square number that has the numbers 121 in that order.

We should notice that:

√121 = 11

Therefore, √1.21 must be 1.1

Simple!

 

 

In this activity, you will find square roots of whole numbers and decimals without using a calculator. 

When finding the square root of a decimal, you will need to relate it to a whole square number. 

When finding a square root, you should ask yourself the question below.

Which of the calculations below are correct square roots?

√36 = 6

√49 = 8

√1 = 1

√10 = 5

Match each square root below to its answer.

Column A

Column B

√49
1.2
√81
9
√1.44
5
√25
7

Which is larger?

 

√100 or 32

32

√100

True or false?

 

√0.04 = 0.16

True

False

What is the square root of 0.36?

Find the value of:

 

√81 - √16 + √9

Finding a square root always makes a number smaller.

 

True or false?

True

False

Which is larger?

 

1.12 or √1.44

1.12

√1.44

Which of these is the correct value of the root below?

 

√2.25

0.15

1.5

15

  • Question 1

When finding a square root, you should ask yourself the question below.

CORRECT ANSWER
EDDIE SAYS
A square root is defined as what you have to multiply by itself to get the number inside the square root sign. e.g. √100 = 10 As 10 x 10 = 100 It's as easy as that!
  • Question 2

Which of the calculations below are correct square roots?

CORRECT ANSWER
√36 = 6
√1 = 1
EDDIE SAYS
The easiest way to spot this is to ask ourselves: "What do you get when you times the answer by itself?" 6 x 6 = 36 so this statement is correct 8 x 8 = 64 not 49, so this statement is not correct 1 x 1 = 1 so this statement is also correct 5 x 5 = 25 not 10, so this statement is also incorrect
  • Question 3

Match each square root below to its answer.

CORRECT ANSWER

Column A

Column B

√49
7
√81
9
√1.44
1.2
√25
5
EDDIE SAYS
Always ask yourself: "What number do I need to multiply by itself to reach this answer?" What can we multiply by itself to reach 49? That's right, 7. 9 x 9 = 81 5 x 5 = 25 √1.44 is a little tricky as it is a decimal. What whole square number can we relate this to? 12 x 12 = 144 So 1.2 x 1.2 = 1.44 Does that make sense?
  • Question 4

Which is larger?

 

√100 or 32

CORRECT ANSWER
√100
EDDIE SAYS
It's impossible to calculate square roots without thinking about square numbers. To solve this question, we need to work out what each number represents: √100 = 10 32 = 9 Which number is larger out of 9 and 10?
  • Question 5

True or false?

 

√0.04 = 0.16

CORRECT ANSWER
False
EDDIE SAYS
0.16 x 0.16 = 0.0256 not 0.04 so this statement is false. You don't even have to work the answer out to solve this one though! We know that we need to find a number that multiplies to 0.04. Would this even be possible if the answer was 0.16?
  • Question 6

What is the square root of 0.36?

CORRECT ANSWER
0.6
EDDIE SAYS
Looking at this decimal, we can see that it is based on the square root of 36. √36 = 6 Therefore, √0.36 is 0.6 Let's check this by working out the reverse: 0.6 x 0.6 should equal 0.36 Does it?
  • Question 7

Find the value of:

 

√81 - √16 + √9

CORRECT ANSWER
8
EDDIE SAYS
Wow, this looks tricky doesn't it?! Let's just take it one step at a time. We have a combination of BODMAS and squares present. We need to work out the square roots (these are 'Orders' in BODMAS) before we add and subtract. This would give us: 9 - 4 + 3 = 8
  • Question 8

Finding a square root always makes a number smaller.

 

True or false?

CORRECT ANSWER
False
EDDIE SAYS
This is true for most, but not all, numbers, If a square root is between 0 and 1, the answer actually gets bigger rather than smaller, so be wary of this. Let's see this in action with a pair of examples: √81 = 9 √0.81 = 0.9 Which number is larger out of 0.9 and 0.81?
  • Question 9

Which is larger?

 

1.12 or √1.44

CORRECT ANSWER
1.12
EDDIE SAYS
If we work out both of these calculations, we find that: 1.12 = 1.21 √1.44 = 1.2 Is 1.2 or 1.21 larger?
  • Question 10

Which of these is the correct value of the root below?

 

√2.25

CORRECT ANSWER
1.5
EDDIE SAYS
This answer is easiest to find by eliminating the options that can't be correct. Is 15 x 15 likely to be 2.25? Are two numbers that are close to 0 (0.15 x 0.15) likely to give the answer 2.25? The answer to both these questions is "no", so 1.5 is the closest and most sensible estimate. Great job on completing this challenge! Why not revise square numbers if you are finding these tricky to identify quickly?
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