Estimating square rootsBetween two whole numbers
Name: Date:
Each root lies between two whole numbers. Write the smaller one.
1292
212
3104
4323
5475
6359
Square roots between integers worksheets
√10 does not come out even, but it is easy to place: it sits between 3 and 4. These free printable worksheets practice just that first step — bracketing an irrational root between the two whole numbers either side.
Kid stuck on one? You don’t just get the sheet.
Square roots between integers
The answer key prints on a separate page.
What's on this sheet
The method never needs a calculator. Name the perfect square just below the number and the one just above — 9 and 16 for √10 — and the root sits between their roots, 3 and 4. Every root on these sheets is irrational, so the answer is always a genuine pair of neighbors rather than a number that comes out on its own.
Why this sheet works
This is the estimating page reduced to its first move, so a child can get the bracketing solid before rounding is added on top. Knowing that √50 is between 7 and 8 is what makes rounding it possible at all, and it is the reading a later Pythagorean answer leans on. The full page mixes in rounding; here every question stops at the two integers.
How this one works
One question from this sheet, worked through a step at a time.
√292
17²=289
18²=324
289<292 < 324
√292is between17 and 18
√292>17
- Find the perfect squares on either side. 289 is 17² and 324 is 18², and 292 sits between them.
- So the root is between those two whole numbers: √292 is between 17 and 18.
- The smaller of the two is 17.