Final answer:
The monomial that squares to give 1 9/16 a¹² b⁶ is 5/4 a⁶ b³.
Step-by-step explanation:
To find the monomial when the expression is the square of that monomial, you need to find the square root of the given expression. In this case, the expression is 1 9/16 a¹² b⁶.
First, convert 1 9/16 to an improper fraction to get 25/16. Now, since we need to find the monomial, which when squared gives this expression, we need to take the square root of both the numeric part and the variable part of the expression. Taking the square root of 25/16 gives us 5/4, and taking the square root of a¹² gives us a⁶, similarly the square root of b⁶ is b³.
Therefore, the monomial that when squared gives 1 9/16 a¹² b⁶ is 5/4 a⁶ b³.