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