Discussion
Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?
*This question is included in Nova Math - Problem Set F: Number Theory, question #21
| (A) | c must be an even number |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 03/27/2013 16:13
Hi I understand everything. However, couldn't it be the case for (b/a) to be a non integer?
If (b/a) is a non integer, then (b/a)^2 will not be a perfect square
If (b/a) is a non integer, then (b/a)^2 will not be a perfect square
Posted: 03/28/2013 01:53
Luigi, great observation. Let me discuss with the question writer.
Posted: 03/28/2013 05:59
Hi Luigi,
When discussing mathematics, fractions are often called perfect squares. For example, 4/9 is a perfect square because it can be written as the square of the fraction 2/3: 4/9 = (2/3)^2.
However, looking at some formal definitions of perfect squares, it does appear that it is often restricted to just integers. So, to avoid ambiguity, we have added the following definition to the question:
A perfect square is an integer or rational number that can be written as the product of two equal factors.
Thanks for pointing this out.
Nova Press
When discussing mathematics, fractions are often called perfect squares. For example, 4/9 is a perfect square because it can be written as the square of the fraction 2/3: 4/9 = (2/3)^2.
However, looking at some formal definitions of perfect squares, it does appear that it is often restricted to just integers. So, to avoid ambiguity, we have added the following definition to the question:
A perfect square is an integer or rational number that can be written as the product of two equal factors.
Thanks for pointing this out.
Nova Press