Estimating Square Roots
Name: _______________________________
Date: _______________________________
Remember: Perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...
To estimate a square root, find the two perfect squares it falls between.
Example: √20 is between √16 and √25, so √20 is between 4 and 5.
Part A: Between Which Two Whole Numbers?
Write the two consecutive whole numbers that each square root falls between.
1.
√8
_______ < √8 < _______
2.
√30
_______ < √30 < _______
3.
√50
_______ < √50 < _______
4.
√75
_______ < √75 < _______
5.
√110
_______ < √110 < _______
6.
√95
_______ < √95 < _______
Part B: Closer To Which Whole Number?
Circle whether each square root is closer to the smaller or larger whole number.
7.
√12
Closer to: 3 or 4
8.
√40
Closer to: 6 or 7
9.
√60
Closer to: 7 or 8
10.
√90
Closer to: 9 or 10
Part C: Order the Square Roots
Arrange these numbers from smallest to largest.
11. √15, 4, √10, 5
_______ < _______ < _______ < _______
12. √80, 9, √70, 10
_______ < _______ < _______ < _______
Part D: Challenge
13. A square has an area of 45 cm². Estimate the length of one side to the nearest whole number.
Side length ≈ _______ cm
14. Which is larger: √50 or 7? Explain your reasoning.
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