Palindromes are numbers that can be written the same way backwards, such as 101 and 12321. You're looking for some numbers which are palindromes, and so are their square numbers.
Alright, I'll give you four of those:
121 is a palindrome, and its square root is 11, both palindromes. 11 x 11 = 121
484 is a palindrome, and its square root is 22, both palindromes. 22 x 22 = 484
10201 is a palindrome, and its square root is 101, both palindromes. 101 x 101 = 10201
12321 is a palindrome, and its square root is 111, both palinromes. 111 x 111 = 12321
Since one-digit are palindromes, just take 1, 4, and 9 because they're perfect. In math, you have to be efficient. Don't think too long about higher numbers. Think about the easier cases first.