How many two-digit squares have the property that the product of their digits is also a square?

Sure, let's solve this step by step:

Step 1: Identify the two-digit squares. They are: 16, 25, 36, 49, 64, 81.

Step 2: Calculate the product of the digits for each of these squares:

• 16: 1*6 = 6
• 25: 2*5 = 10
• 36: 3*6 = 18
• 49: 4*9 = 36
• 64: 6*4 = 24
• 81: 8*1 = 8

Step 3: Check which of these products are squares:

• 6 is not a square.
• 10 is not a square.
• 18 is not a square.
• 36 is a square.
• 24 is not a square.
• 8 is not a square.

So, only one two-digit square (49) has the property that the product of its digits is also a square.