A square root between two whole numbers

Difficulty Starter · Set ou0r7q

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1
The square root of 13 lies between two whole numbers. What is the smaller of them?
2
The square root of 6 lies between two whole numbers. What is the smaller of them?
3
The square root of 6 lies between two whole numbers. What is the smaller of them?
4
The square root of 32 lies between two whole numbers. What is the smaller of them?
5
The square root of 24 lies between two whole numbers. What is the smaller of them?
6
The square root of 15 lies between two whole numbers. What is the smaller of them?
7
The square root of 15 lies between two whole numbers. What is the smaller of them?
8
The square root of 21 lies between two whole numbers. What is the smaller of them?
9
The square root of 12 lies between two whole numbers. What is the smaller of them?
10
The square root of 38 lies between two whole numbers. What is the smaller of them?
11
The square root of 17 lies between two whole numbers. What is the smaller of them?
12
The square root of 5 lies between two whole numbers. What is the smaller of them?
13
The square root of 47 lies between two whole numbers. What is the smaller of them?
14
The square root of 27 lies between two whole numbers. What is the smaller of them?
15
The square root of 19 lies between two whole numbers. What is the smaller of them?
16
The square root of 43 lies between two whole numbers. What is the smaller of them?
17
The square root of 45 lies between two whole numbers. What is the smaller of them?
18
The square root of 10 lies between two whole numbers. What is the smaller of them?
19
The square root of 12 lies between two whole numbers. What is the smaller of them?
20
The square root of 19 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 48.
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 40 different ones, 17% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

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.

Next to this

A negative index as a fraction

Numbers 1–5; every one will carry a negative index.

Dividing powers of one base

Numbers 2–5.

All of powers and roots

12 skills in this topic, 36 sets between them.

Printing it

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