Final Answer:
The numerator and denominator of the fraction equivalent to (1.5)², both being square numbers between 1 and 100, are 9 and 4, respectively.
Step-by-step explanation:
The expression (1.5)² can be calculated by simply squaring 1.5, which is 2.25. To represent this as a fraction with square numbers between 1 and 100 as the numerator and denominator, 2.25 needs to be expressed in such a form.
Considering that 2.25 = 9/4, it satisfies the conditions. Here, 9 is a square number (3² = 9), and 4 is also a square number (2² = 4). Therefore, (1.5)² is equivalent to the fraction 9/4.
To confirm this, when you square 1.5, it results in 2.25. Now, simplify 2.25 to its fractional form, which is 9/4. The numerator, 9, is a perfect square as 3² = 9, and the denominator, 4, is also a square number as 2² = 4. Thus, the fraction 9/4 fulfills the condition of having both its numerator and denominator as square numbers between 1 and 100 while representing the value of (1.5)².