38. While doing his homework, Petya was in a hurry to get to football and, as always in such cases, made mistakes. Instead of squaring the number, he doubled it and got a two-digit number, written with the same digits as the required square, only in reverse order. What is the correct answer that Petya should have obtained?
38. Let Pete need to square the number $x$. He should have obtained $x^{2}=10 a+b$, but in fact, he got $2 x=10 b+a$. This means $x=\frac{10 b+a}{2}$. From this, it follows that the number $x$ is a single-digit number (since $x^{2}$ is a two-digit number), and the number $10 b+a$ is an even two-digit number. The number $10 b+a$ should be sought among the numbers 12, $14,16,18$. The condition of the problem is satisfied only by the number 18. Therefore, $x=18: 2=$ $=9$ and $x^{2}=81$. Pete should have obtained 81, but he got 18.