Query about Q.5 from "(I'm Overwhelmed) Arithmetic Progress Quiz #7" [7007]

https://www.gregmat.com/quizzes/quiz/im-overwhelmed-arithmetic-progress-quiz-7 (Question 5)


for the last last option in this question, root five over nine, cant we square both the numerator and denominator or does that violate a rule?

No we can’t.

You would be essentially solving a totally different question.