11+ style maths

[jahiddbest]

There are eight square numbers containing one or two digits. What are they? Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?

 

[Deleted member 4993]

There are eight square numbers containing one or two digits. What are they? Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?

There are eight square numbers containing one or two digits

What is the definition of square numbers?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[JeffM]

Are you sure that you have given us the EXACT wording of the second question?

By the way, I see no mathematical point to the second question.

 

[pka]

There are eight square numbers containing one or two digits. What are they? Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?

If we define a square number as an natural number times itself, then I get ten one or two digit squares:
$0,~1,~4,~9,~16,~25,~36,~49,~64,~\&~81$

 

[Otis]

If we define a square number as [a] natural number times itself, then I get ten … squares …

Using that definition, I get nine squares.

 

[Dr.Peterson]

Since the question doesn't mention natural numbers, that isn't what matters. What's important is whether 0 counts as a 1-digit number. But in any case, the problem is clearly wrong. Maybe they don't consider 1 to be a square?

The second part likewise has no answer, unless they allow 000 or 001 and so on. Where did these come from?

 

[JeffM]

Oh, I suspect the second question has an expected answer. It is why I asked whether the second question we were asked is the correct question. I suspect the actual question asked which three-digit square numbers could be made in either of those ways. If so, the expected answers would include

4^2 * 10 + 3^2 = 160 + 9 = 169 = 13^2.

6^2 * 10 + 1^2 = 360 + 1 = 19^2.

I did not bother to look for more because I see no mathematical point to the exercise.

 

[Otis]

… [defining the set of Natural numbers] isn't what matters …

That's at the very heart of what I'd razzed pka about. Were you addressing him also? (I can't always tell because sometimes you don't quote a source, with your comments.)

?

 

[Dr.Peterson]

That's at the very heart of what I'd razzed pka about. Were you addressing him also? (I can't always tell because sometimes you don't quote a source, with your comments.)

?

Yes, I was referring to the natural number issue (0 or not), replying to both of you, and intentionally not singling out one. But mostly I was talking to pka, to say that the issue doesn't need to be raised here at all.

Oh, I suspect the second question has an expected answer. It is why I asked whether the second question we were asked is the correct question. I suspect the actual question asked which three-digit square numbers could be made in either of those ways. If so, the expected answers would include

4^2 * 10 + 3^2 = 160 + 9 = 169 = 13^2.

6^2 * 10 + 1^2 = 360 + 1 = 19^2.

I did not bother to look for more because I see no mathematical point to the exercise.

I assume you are talking about a reworded version of the problem, where you are changing "Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?" to "Which three-digit square numbers can be made either (a) by putting a one-digit square number in front of a two-digit square number or (b) by putting a two-digit square number in front of a one-digit square number?"

As I read the problem, it requires a single number to be made in both ways, e.g. 004 = 00 4 = 0 04.

And I agree that it is a pointless problem either way.

 

[JeffM]

I assume you are talking about a reworded version of the problem, where you are changing "Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?" to "Which three-digit square numbers can be made either (a) by putting a one-digit square number in front of a two-digit square number or (b) by putting a two-digit square number in front of a one-digit square number?"

As I read the problem, it requires a single number to be made in both ways, e.g. 004 = 00 4 = 0 04.

And I agree that it is a pointless problem either way.

Oh you are indeed reading what it literally says. I was trying to make sense of it in the way you interpreted me. But though it has answers, I do not see that it teaches anything.

 

[Otis]

Regarding the second question, I think it's too much of a hack to call numbers like 00 and 04 two-digit squares.

I think it's more likely that somebody screwed up (possibly, by looking at 169 and mistakenly thinking of 69 as a square -- confusing it with 64).

If the second question were to have a valid answer, then the point in assigning it could simply be to get young people to think. As it turned out, we're doing the thinking, ha.

 

[HallsofIvy]

There are eight square numbers containing one or two digits. What are they?

Well, first of all this is NOT true! There are nine square numbers containing one or two digits. You can get them by simply squaring the numbers from 1 to 9:
1, 4, 9, 16, 25, 36, 49, 64, 81.

Which three-digit square number can be made either by putting a one-digit square number in front of a two-digit square number or by putting a two-digit square number in front of a one-digit square number?

So DO IT! The one digit square numbers are 1, 4, and 9. The two digit square numbers are 16, 25, 36, 49, 64, and 81. So there are 3*6= 18 three digit numbers you can get by putting one of 1, 4, or 9 followed by 16, 36, 49, 64, or 81:
116, 136, 149, 164, 181, 416, 436, 449, 464, 481, 916, 936, 949, 964, and 981.
Are any of those square numbers?

Similarly for "a two digit square number in front of a one digit square number".