The answer is the book is approximately 15.3 inches tall, and it will fit on the shelf, since 16 inches is greater than 15.3 inches.
Here's an explanation:
The problem has already said that the book shelf is 16 inches tall. It's given that the area of the front cover of a square book is 234 square inches. Since the book is square, the length of the book will be equal to the width of the book. So, the find the length of the book, you would find the square root of 234, since both sides would be the same, and you'd get an answer of approximately 15.3 inches. If the length of the book is 15.3 inches, then it would fit on the book shelf, since 15.3 inches is less than 16 inches.