Estimating Square Roots
Name: _________________________
Date: _________________________
Instructions: Estimate each square root to the nearest whole number. Remember: find which two perfect squares your number falls between, then decide which is closer.
Example: √50 is between √49 = 7 and √64 = 8. Since 50 is closer to 49, √50 ≈ 7
Part A: Between Which Perfect Squares?
Fill in the blanks to show which two perfect squares each number falls between.
1.
____² < 20 < ____²
so _____ < √20 < _____
2.
____² < 75 < ____²
so _____ < √75 < _____
3.
____² < 110 < ____²
so _____ < √110 < _____
4.
____² < 38 < ____²
so _____ < √38 < _____
Part B: Estimate to the Nearest Whole Number
5. √10 ≈ _____
6. √28 ≈ _____
7. √55 ≈ _____
8. √90 ≈ _____
9. √15 ≈ _____
10. √99 ≈ _____
11. √42 ≈ _____
12. √130 ≈ _____
13. √68 ≈ _____
14. √8 ≈ _____
15. √120 ≈ _____
16. √47 ≈ _____
Part C: Challenge Problems
17. A square has an area of 85 cm². Estimate the length of one side to the nearest whole number.
Side length ≈ ________ cm
18. Which whole number is √52 closest to? __________
19. True or False: √80 is closer to 8 than to 9. __________
20. Order these values from smallest to largest: √30, 5, √50, 6
_________ , _________ , _________ , _________