Answer:
4 and 9
Step-by-step explanation:
A square number the product of an integer multiplied by itself.
If the product of two consecutive square numbers is 36, then we are looking for square numbers less than 36 that are factors of 36.
The square numbers that are less than 36 are:
[tex]1^2 = 1 \\\\2^2 = 4\\\\ 3^2 = 9 \\\\ 4^2 = 16 \\\\ 5^2 = 25[/tex]
The factors pairs of 36 are:
[tex]1\; \rm and\;36\\\\ 2 \; and \;18\\\\3\;and\;12\\\\4\;and\;9[/tex]
As 4 and 9 are consecutive square numbers that multiply to 36, then the two numbers are:
[tex]\LARGE\boxed{\boxed{\rm 4\;and\;9}}[/tex]
