Estimating square rootsTo one decimal place
Name: Date:
Round each root to one decimal place.
1357
2439
3237
441
5343
6239
Square roots to one decimal place worksheets
Once a root is bracketed between two whole numbers, the next question is which it is closer to — and then, closer still, what it is to one decimal place. These free printable worksheets practice that finer estimate.
Kid stuck on one? You don’t just get the sheet.
Square roots to one decimal place
The answer key prints on a separate page.
What's on this sheet
√10 is 3.2 because 3.2² is 10.24 and 3.1² is 9.61 — squaring two candidates and picking the closer is the whole method, and it works on any root without a calculator. Every root here is irrational, and none lands on a borderline: a value whose square puts it exactly halfway is left out, because there would be no honest answer to give.
Why this sheet works
This is the harder half of the estimating skill, split off so it can be practiced on its own. The bracketing page stops at the two integers either side; this one carries the estimate to a tenth, which is the form a real measurement or a Pythagorean length usually needs. Working the square of a guess, rather than halving and hoping, is the habit these sheets build.
How this one works
One question from this sheet, worked through a step at a time.
√357
18²=324
19²=361
324<357 < 361
√357is between18 and 19
18.8²=353.44
18.9²=357.21
19²=361
√357≈18.9
- Find the perfect squares on either side. 324 is 18² and 361 is 19², and 357 sits between them.
- So the root is between those two whole numbers: √357 is between 18 and 19.
- Now try tenths. 18.9² = 357.21, and the neighbors are 18.8² = 353.44 and 19² = 361. 357 is closest to 357.21, so √357 ≈ 18.9.