Final answer:
A perfect square monomial is an expression that can be expressed as the square of a polynomial. From the given options, 121; 11, 4x²; 2x, and 49x⁴; 7x² are perfect squares with their respective square roots being 11, 2x, and 7x².
Step-by-step explanation:
When identifying a perfect square monomial and its square root, we are looking for expressions that can be written in the form of a base raised to an even exponent, which in this case is 2. A monomial is a perfect square if it can be expressed as the square of a polynomial. Its square root is the polynomial that when squared gives back the original monomial.
- 121; 11 is a perfect square monomial since 112 = 121.
- 4x²; 2x is a perfect square monomial since (2x)² = 4x².
- The expression 9x²-1; 3x-1 is not a monomial but rather a binomial, and thus cannot be a perfect square monomial.
- 25x; 5x is not a perfect square monomial since the variable x is not raised to an even power.
- 49x⁴; 7x² is a perfect square monomial since (7x²)² = 49x⁴.