Perfect Squares

Directions: Using the digits 1- 9, at most one time each, to fill in the boxes to make each expression evaluate to a perfect square number.

Extension/Challenge: What is the largest/smallest square number you can make? How many different perfect square numbers could be made?

You may find it helpful to factor each number in the expression into their prime factors first.

Number of Unique Solutions: 12

#1:
18 x 1 x 2 = 36
2 x 14 x 7 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 3 x 2 x 9 = 324

#2:
18 x 1 x 2 = 36
7 x 14 x 2 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 3 x 2 x 4 = 144

#3:
18 x 1 x 2 = 36
7 x 14 x 8 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 3 x 2 x 9 = 324

#4:
18 x 1 x 2 = 36
8 x 14 x 7 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 4 x 2 x 3 = 144

#5:
18 x 4 x 2 = 144
7 x 14 x 2 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 3 x 2 x 1 = 36

#6:
18 x 4 x 2 = 144
7 x 14 x 2 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 9 x 2 x 3 = 324

#7:
18 x 4 x 2 = 144
7 x 14 x 8 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 3 x 2 x 1 = 36

#8:
18 x 4 x 2 = 144
8 x 14 x 7 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 9 x 2 x 3 = 324

#9:
18 x 9 x 2 = 324
7 x 14 x 2 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 3 x 2 x 1 = 36

#10:
18 x 9 x 2 = 324
7 x 14 x 2 = 196
5 x 15 x 3 = 225
2 x 8 = 16
6 x 4 x 2 x 3 = 144

#11:
18 x 9 x 2 = 324
7 x 14 x 8 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 3 x 2 x 1 = 36

#12:
18 x 9 x 2 = 324
7 x 14 x 8 = 784
5 x 15 x 3 = 225
2 x 2 = 4
6 x 3 x 2 x 4 = 144

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