which expressions represent a perfect square monomial and its square root? check all that apply. 121; 11…

Explanation:

Step1: Recall perfect - square monomial rule

A perfect - square monomial is of the form (a^{2}x^{2n}), and its square root is (ax^{n}), where (a) is a constant and (n) is a non - negative integer.

Step2: Check 121; 11

Since (11\times11 = 121), (121) is a perfect - square monomial and its square root is (11).

Step3: Check (4x^{2}); (2x)

Since ((2x)\times(2x)=4x^{2}), (4x^{2}) is a perfect - square monomial and its square root is (2x).

Step4: Check (9x^{2}-1); (3x - 1)

((3x - 1)(3x - 1)=9x^{2}-6x + 1\neq9x^{2}-1), so (9x^{2}-1) is not a perfect - square monomial with square root (3x - 1).

Step5: Check (25x); (5x)

Since ((5x)\times(5x)=25x^{2}\neq25x), (25x) is not a perfect - square monomial with square root (5x).

Step6: Check (49x^{4}); (7x^{2})

Since ((7x^{2})\times(7x^{2})=49x^{4}), (49x^{4}) is a perfect - square monomial and its square root is (7x^{2}).

Answer:

121; 11 4x²; 2x 49x⁴; 7x²