Estimating square rootsTo the nearest whole number
Name: Date:
Round each root to the nearest whole number.
1200
2111
3162
472
5278
6268
Estimating square roots worksheets
√10 does not come out — so how big is it? These free printable worksheets teach the one method that works on any root: bracket it between the two perfect squares you already know.
Kid stuck on one? You don’t just get the sheet.
Estimating square roots
The answer key prints on a separate page.
What's on this sheet
√10 sits between √9 and √16, so it sits between 3 and 4. That is the whole method, it needs no calculator, and it works on a root a child has never seen. Knowing which perfect squares a number falls between is the only thing being asked, and every sheet here opens there.
Why this sheet works
Rounding to the nearest whole number is a real second step, not a harder version of the first. For √10 the bracket and the rounded value are both 3; for √15 they are 3 and 4. Deciding which end needs the midpoint — and the midpoint is a SQUARE: 3.5² is 12.25, so anything above that rounds up. Halving 3 and 4 and then guessing is the shortcut that gets the borderline cases wrong.
How this one works
One question from this sheet, worked through a step at a time.
√200
14²=196
15²=225
196<200 < 225
√200is between14 and 15
14.5²=210.25
200<210.25
√200≈14
- Find the perfect squares on either side. 196 is 14² and 225 is 15², and 200 sits between them.
- So the root is between those two whole numbers: √200 is between 14 and 15.
- Which end is it nearer? Halfway between 14 and 15 is 14.5, and 14.5² is 210.25. 200 is below that, so the root is nearer 14.