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Estimate Powers and Roots

In this worksheet, students will estimate answers to roots and squares.

'Estimate Powers and Roots' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

A lot of the time, when we aren't using a calculator, we can't get exactly correct answers to questions. In these instances, we have to estimate answers.

Estimating means "making an educated guess". This time, we're going to look at how we do this with square numbers and square roots.

 

Square numbers:

To be able to do this, we must know our square numbers up to 102. These are 1,4,9,16, 25, 36, 49, 64, 81 and 100

 

Example 1: Estimating a square root

Which two integers does √80 lie?

To do this, we need to look at which square numbers 80 is. We can see it is between 64 and 81.

As √64 = 8 and √81 = 9, √80 must be between 8 and 9 (as 80 is closer to 81 than 64, √80 will be very close to 9)

 

Example 2: Estimating a square number

Which two squares will 7.12 lie?

Again, we need to look at our square numbers. 7.1 is between 7 and 8

With 72 = 49 and 82 = 64

Therefore, 7.12 must be between 49 and 64

Match the square numbers.

Column A

Column B

52
4
62
64
82
25
22
36

Match these square roots with their positive value.

Column A

Column B

√ 25
9
√ 1
1
√ 81
10
√ 100
5

√67 will be between which two integers?

Column A

Column B

√ 25
9
√ 1
1
√ 81
10
√ 100
5

3.72 will be between which two square numbers?

Column A

Column B

√ 25
9
√ 1
1
√ 81
10
√ 100
5

Find the error in the following calculation:

8.22

Select 'Correct' if the line is ok, select 'incorrect' if there is an error in the line.

Find the error in the following calculation:

√40

Select 'Correct' if the line is ok, select 'incorrect' if there is an error in the line.

Which two numbers does √99 lie?

7 and 8

8 and 9

9 and 10

Find an estimate for √42

 

Give your answer to 1 decimal place.

7 and 8

8 and 9

9 and 10

Is √15 closer to 3 or 4?

3

4

Estimate the answer to 8.22

 

Give your answer to the nearest whole number.

3

4

  • Question 1

Match the square numbers.

CORRECT ANSWER

Column A

Column B

52
25
62
36
82
64
22
4
EDDIE SAYS
Remember that squared means times a number by itself. For example 32 = 3 x 3 = 9
  • Question 2

Match these square roots with their positive value.

CORRECT ANSWER

Column A

Column B

√ 25
5
√ 1
1
√ 81
9
√ 100
10
EDDIE SAYS
To find a square root, ask the question "what do I need to times by itself to get this?" For example, 36 = 6 x 6 So, √36 = 6
  • Question 3

√67 will be between which two integers?

CORRECT ANSWER
EDDIE SAYS
Think, which two square numbers are 67 between? You can begin by reasoning that 67 is between 64 and 81.
  • Question 4

3.72 will be between which two square numbers?

CORRECT ANSWER
EDDIE SAYS
If 3.7 is between 3 and 4. 3.72 must be between... This is good practise, let's keep going!
  • Question 5

Find the error in the following calculation:

8.22

Select 'Correct' if the line is ok, select 'incorrect' if there is an error in the line.

CORRECT ANSWER
EDDIE SAYS
The mistake here is in line 2, does the little 2 mean times by 2 or times by itself? This error then follows through to the last line, as 8.2 x 8.2 is actually 67.24.
  • Question 6

Find the error in the following calculation:

√40

Select 'Correct' if the line is ok, select 'incorrect' if there is an error in the line.

CORRECT ANSWER
EDDIE SAYS
If you are estimating a square root, can you say exactly what the answer is?
  • Question 7

Which two numbers does √99 lie?

CORRECT ANSWER
9 and 10
EDDIE SAYS
Remember to look for the square numbers this is between. 99 is between 81 and 100.
  • Question 8

Find an estimate for √42

 

Give your answer to 1 decimal place.

CORRECT ANSWER
EDDIE SAYS
We can see that @radic;42 must lie between 6 and 7. As 42 is around the middle of 36 and 49, but a bit closer to 36, any answer between 6.3 and 6.6 is acceptable. The exact answer is 6.481.
  • Question 9

Is √15 closer to 3 or 4?

CORRECT ANSWER
4
EDDIE SAYS
We can see that √15 is between √9 (3) and √1 (4). It is a lot closer to √16 than √9 so √15 must be closer to 4. This should be beginning to make sense now. If you're not feeling confident, go back to the introduction page and make some notes for your revision.
  • Question 10

Estimate the answer to 8.22

 

Give your answer to the nearest whole number.

CORRECT ANSWER
EDDIE SAYS
We can see that 8.22 is between 64 and 81. As 8.2 is closer to 8 than 9, 8.22 is going to be closer to 82 (64) than 92 (81) You can give any value from 66-69 as your answer. The exact answer is 67.24. Well done, that’s another activity completed!
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