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Calculate Square Roots (Without a Calculator)

In this worksheet, students will practise finding the square roots of whole numbers and simple decimals.

'Calculate Square Roots (Without a Calculator)' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Square roots are another 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 get the number"

 

For example, if I was trying to find √81

I would ask "what do I multiply by itself to get 81?" the answer is 9

So √81 = 9

 

Square roots of decimals:

If you were ever asked to find the square root of a decimal without a calculator, it would be a simple one that was based around the square number you should already know.

For example: 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

So therefore

√1.21 must be 1.1

When finding a square root, you have to ask "what number do I have to multiply by _________ to get this number?"

Which of these values are correct square roots?

√36 = 6

√49 = 8

√1 = 1

√10 = 5

Match the square root to their answers.

Column A

Column B

√49
9
√81
7
√1.44
5
√25
1.2

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

Square rooting, 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 √2.25

0.15

1.5

15

  • Question 1

When finding a square root, you have to ask "what number do I have to multiply by _________ to get this number?"

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.
  • Question 2

Which of these values are correct square roots?

CORRECT ANSWER
√36 = 6
√1 = 1
EDDIE SAYS
Again, the easiest way to spot this is to ask what you get when you times the answer by itself. For example is 5 x 5 = 10? No, so √10 does not equal 5.
  • Question 3

Match the square root to their answers.

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 get this? What do I need to multiply by itself to get 49? 7
  • Question 4

Which is larger?

√100 or 32

CORRECT ANSWER
√100
EDDIE SAYS
It's impossible to do square roots without thinking about square numbers, To solve this question, you just need to work out what each number represents. √100 = 10 32 = 9
  • Question 5

True or false?

√0.04 = 0.16

CORRECT ANSWER
False
EDDIE SAYS
You don't even have to work the answer out to solve this, 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, we can see that it is based on the square root of 36 (which is 6), so our answer must be 0.6.
  • Question 7

Find the value of...

√81 - √16 + √9

CORRECT ANSWER
8
EDDIE SAYS
Again, we have a combination of BODMAS and squares. We need to work out the square roots (these are orders) before we add and subtract. This would give us 9 - 4 + 3 = 8.
  • Question 8

Square rooting, always makes a number smaller.

 

True or False?

CORRECT ANSWER
False
EDDIE SAYS
This is true for most numbers but not all numbers, If you square root a number between 0 and 1, the answer is actually bigger so be wary of this.
  • Question 9

Which is larger?

1.12 or √1.44

CORRECT ANSWER
1.12
EDDIE SAYS
We simply have to work these both out. 1.12 = 1.21 √1.44 = 1.2
  • Question 10

Which of these is the correct value of √2.25

CORRECT ANSWER
1.5
EDDIE SAYS
This is easiest to do by eliminating the options that can't be correct. Ask if 15 x 15 is 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?
---- OR ----

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