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Given,

Number of pages in the book that is total cases = 90 pages

Number of perfect squares from 1 to 90 are 1, 4, 9, 16, 25, 36, 49, 64, 81.

Favorable cases, that is number of perfect squares between 1 to 90 = 9

[Probability is defined as the ratio of number of favourable outcomes to the number of total possible outcomes]

Probability of a page number is a perfect square $ = \dfrac{9}{{90}} = \dfrac{1}{{10}}$

Therefore, probability is $\dfrac{1}{{10}}$.