which monomials are perfect squares? select three options.\n$6x^{2}$\n$9x^{8}$\n$17x^{9}$\n$25x^{12}$\n$36x^{…

Explanation:

Step1: Recall perfect - square rule

A monomial $ax^n$ is a perfect square if $a$ is a perfect - square number and $n$ is an even non - negative integer.

Step2: Analyze $6x^2$

The coefficient $6$ is not a perfect square ($\sqrt{6}$ is not an integer), so $6x^2$ is not a perfect - square monomial.

Step3: Analyze $9x^8$

The coefficient $9 = 3^2$ and the exponent of $x$ is $8$ (an even number). So, $9x^8=(3x^4)^2$ is a perfect - square monomial.

Step4: Analyze $17x^9$

The coefficient $17$ is not a perfect square ($\sqrt{17}$ is not an integer) and the exponent of $x$ is $9$ (an odd number), so $17x^9$ is not a perfect - square monomial.

Step5: Analyze $25x^{12}$

The coefficient $25 = 5^2$ and the exponent of $x$ is $12$ (an even number). So, $25x^{12}=(5x^6)^2$ is a perfect - square monomial.

Step6: Analyze $36x^{16}$

The coefficient $36 = 6^2$ and the exponent of $x$ is $16$ (an even number). So, $36x^{16}=(6x^8)^2$ is a perfect - square monomial.

Answer:

B. $9x^8$, D. $25x^{12}$, E. $36x^{16}$