ESTIMATING Square Roots
Vocabulary
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Square Root: will be a positive and negative value
o When written in words “what is the square root of 36” write as +6 and -6
Principal Square Root- is used with the √49 - only give positive value (+7)
Negative square root = -√49 = -7 (notice the negative sign is outside of the√ sign!
What is the square root of 20? (√20)
Find the perfect squares before and after the √20
√ 16
4
< √20 < √25
< √20 <
5
List the square roots from 16 to 25 (number line)
√16 √17 √18 √19 √20 √21 √22 √23 √24 √ 25
4
4.5
5
Find the middle value (like you do with median)
Is the estimated square root before or after the
middle value?
√20≈4.45
The estimated value of √20 is before the 4.5
The √20 is very close to the 4.5. My estimate is 4.45 or 4.4
Estimate the √108
√100√101√102√103√104√105√106√107√108√109√110√111√112√113√114√115√116√117√118√119√120√121
10
10.25
10.37 10.4
10.5
First I found the middle
The √108 is before the middle point (10.5)
Then I found the middle of the lower half (10.25)
Then I found the middle point between the 10.25 and 10.5 (10.37)
√108 is really close to 10.37. It must be 10.4
To show your work,
1.)
2.)
3.)
4.)
√ 100 <√ 108 < √121
10 < √108 <11
Number line work - find the median then estimate
√108 ≈ 10.4
10.75
11