Directions: Using the digits 0-9 at most one time each, make both of these equations true.

### Hint

What are some two digit numbers that have a perfect square as a factor?

### Answer

Multiple answers. Here is one possibility:

Number of Unique Solutions: 8

1: sqrt(16) = 2sqrt(4) and sqrt(9) = 3

2: sqrt(18) = 3sqrt(2) and sqrt(49) = 7

3: sqrt(54) = 3sqrt(6) and sqrt(81) = 9

4: sqrt(64) = 8sqrt(1) and sqrt(9) = 3

5: sqrt(72) = 3sqrt(8) and sqrt(16) = 4

6: sqrt(81) = 3sqrt(9) and sqrt(4) = 2

7: sqrt(09) = 3sqrt(1) and sqrt(64) = 8

8: sqrt(98) = 7sqrt(2) and sqrt(16) = 4

Source: Jonathan Newman

I think there are only three solutions. The one in the example and

Sqrt(18) = 3*Sqrt(2) ; Sqrt(49) = 7

Sqrt(98) = 7*Sqrt(2) ; Sqrt(16) = 4

Two additional possibilities:

09=3√1

√64=8

√64=8√1

√09=3

sq root of 64 equals 8 sq root 1

sq root of 49 equals 7