Question

The difference between two square numbers is 19. What are the two square numbers?

Answer 1

There;s actually a pattern in the difference between two consecutive square numbers. So the first two squared numbers
1 and 4. 4 - 1 = 3
Next one
4 and 9. 9 - 4 = 5
9 and 16. 16 - 9 = 7
16 and 25. 25 - 16 = 9
25 and 36. 36 - 25 = 11
See a pattern? Bet you can then find the two that are 19 apart :3

Answer 2

\(\begin{matrix}
\text{Psymon}\\

\text{1 and 4. 4 - 1 =}&\text{3}\\
\text{Next one}\\
\text{4 and 9. 9 - 4 =}&\text{ 5}\\
\text{9 and 16. 16 - 9 =}&\text{ 7}\\
\text{16 and 25. 25 - 16 =}&\text{ 9}\\
\text{25 and 36. 36 - 25 =}&\text{ 11}\\

\end{matrix}\)

See a pattern?

Answer 3

OK, is there a formula such as 2n + 1 or anything like that?

Answer 4

I suppose you could put it like that, where n is the number you are squaring. That would give us as n =9, which of course the difference between 9^2 and 10^2 is the desired 19. That makes more sense like that :3

Answer 5

Is the difference always a prime number?

Answer 6

i am more confused now, i am 11 years old can you simplify your answer

Answer 7

Or is the difference always the sum of the two numbers:
1+2 = 3
2+3 = 5
etc

Answer 8

rionogal, the two numbers are 9 and 10 right?

Answer 9

no

Answer 10

Let's see 9 x 9 = 81 and 10 x 10 = 100

100 - 81 = 19 right?

Answer 11

ok i get it now, thanks

Answer 12

oo neat pattern :o