Question

which monomials are perfect squares? select three options. 6x² 9x⁸ 17x⁹ 25x¹² 36x¹⁶

Explanation:

Step1: Recall perfect square monomial rule

A monomial \(ax^n\) is a perfect square if \(a\) is a perfect square and \(n\) is even.

Step2: Check \(6x^2\)

\(6\) is not a perfect square (\(\sqrt{6}\) is not integer), so \(6x^2\) is not a perfect square.

Step3: Check \(9x^8\)

\(9 = 3^2\) (perfect square), \(8\) is even. So \(9x^8=(3x^4)^2\), a perfect square.

Step4: Check \(17x^9\)

\(17\) is not a perfect square, \(9\) is odd. So \(17x^9\) is not a perfect square.

Step5: Check \(25x^{12}\)

\(25 = 5^2\) (perfect square), \(12\) is even. So \(25x^{12}=(5x^6)^2\), a perfect square.

Step6: Check \(36x^{16}\)

\(36 = 6^2\) (perfect square), \(16\) is even. So \(36x^{16}=(6x^8)^2\), a perfect square.

Answer:

B. \(9x^8\), D. \(25x^{12}\), E. \(36x^{16}\)