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

Several answers are possible including:

18 x 9 x 2 = 324

2 x 14 x 7 = 196

5 x 15 x 3 = 225

2 x 8 = 16

6 x 3 x 2 x 4 = 144

18 x 9 x 2 = 324

2 x 14 x 7 = 196

5 x 15 x 3 = 225

2 x 8 = 16

6 x 3 x 2 x 4 = 144

and

18 x 1 x 2 = 36

8 x 14 x 7 = 784

5 x 15 x 3 = 225

2 x 2 = 4

6 x 3 x 2 x 9 = 324

and

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

Source: Erick Lee

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.

Thanks for sharing your solution Robert – I’ve added it to the other answers 🙂