Estimating Non-Perfect Square Roots

Name: _______________________________

Date: _______________________________

Remember: Perfect squares are numbers like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...

When a number is NOT a perfect square, its square root falls between two whole numbers.

Example: √20 is between 4 and 5, because 4² = 16 and 5² = 25

Part A: Between Which Two Whole Numbers?

Write the two consecutive whole numbers that each square root falls between.

1. √10 is between _______ and _______

2. √30 is between _______ and _______

3. √50 is between _______ and _______

4. √75 is between _______ and _______

5. √92 is between _______ and _______

6. √40 is between _______ and _______

Which whole number is each square root closest to? Circle your answer.

7. √12 is closest to: 3 or 4

8. √28 is closest to: 5 or 6

9. √60 is closest to: 7 or 8

10. √85 is closest to: 9 or 10

11. If √n is between 6 and 7, what are the smallest and largest whole number values n could be?

Smallest: _______ Largest: _______

12. Estimate √45 to one decimal place by testing values. Show your working:

√45 ≈ _______