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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?

Hint

Hint

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

Answer

Answer

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

Source: Erick Lee

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4 comments

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

    I used factors of the given numbers and then matched them up to make sure that there were two of each which would make them perfect squares.

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