How to Determine if a Square Root is a Perfect Square

In order to determine if a square root is a perfect square, you must find a number that can be multiplied by itself to get the square root of the number. This original number of the square root is called a perfect square when some number times itself is equal to this number.

Instructions

How to Determine if a Square Root is a Perfect Square

1. List all the factor sets (example: 4, 6) of the number underneath the square root using the multiplication symbol (x). An example would be 4x6. We will use this as our working example: the square root of 36. The square root of 36 would yield the following factor sets: 1x36, 2x18, 3x12, 4x9, and 6x6.

2. Look at the numbers to see if one of the factor sets has the same number twice. Examples of these type of factor sets would be 8x8 or 6x6. Continuing with the same working example, the square root of 36, we see that one of the factor sets listed in step one does has the same number twice. This factor set is 6x6.

3. Conclude that it is a perfect square if one of the factor sets has the same number twice. We can see from our working example that it is a perfect square because we found 6x6 to be one of the factor sets. 6x6 is a factor set that has the same number twice.

Tips & Warnings

• Note: If there had not been a factor set that had the same number twice, then the number underneath the square root would not be a perfect square.