A square root between two whole numbers

Difficulty Stretch · Set uz9xlo

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1
The square root of 90 lies between two whole numbers. What is the smaller of them?
2
The square root of 320 lies between two whole numbers. What is the smaller of them?
3
The square root of 327 lies between two whole numbers. What is the smaller of them?
4
The square root of 35 lies between two whole numbers. What is the smaller of them?
5
The square root of 406 lies between two whole numbers. What is the smaller of them?
6
The square root of 427 lies between two whole numbers. What is the smaller of them?
7
The square root of 368 lies between two whole numbers. What is the smaller of them?
8
The square root of 72 lies between two whole numbers. What is the smaller of them?
9
The square root of 307 lies between two whole numbers. What is the smaller of them?
10
The square root of 72 lies between two whole numbers. What is the smaller of them?
11
The square root of 11 lies between two whole numbers. What is the smaller of them?
12
The square root of 7 lies between two whole numbers. What is the smaller of them?
13
The square root of 192 lies between two whole numbers. What is the smaller of them?
14
The square root of 85 lies between two whole numbers. What is the smaller of them?
15
The square root of 13 lies between two whole numbers. What is the smaller of them?
16
The square root of 6 lies between two whole numbers. What is the smaller of them?
17
The square root of 19 lies between two whole numbers. What is the smaller of them?
18
The square root of 129 lies between two whole numbers. What is the smaller of them?
19
The square root of 329 lies between two whole numbers. What is the smaller of them?
20
The square root of 138 lies between two whole numbers. What is the smaller of them?

What is in this set

The numbers in this set run from 5 to 436.
Every problem in it will fall between two square numbers.
A careful solution takes 2 written steps on average.
The mistake this set invites most often, in 100% of the problems: that is the larger one.
Answers are a whole number.

Drawing 240 problems from this page produced 172 different ones, 72% — so a sheet of 20 is a new sheet almost every time.

The same skill, harder or easier

We would put this in front of a grade 7 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.

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Printing it

The printed sheet carries no menus and no advertising, and the answer key is on its own page.