1. You can easily calculate the square-root of a number if this number is a square:

2. If the number is not a square (75 is not a square of a rational number) you can express as an approximation in decimal form. You have then a result with a lot of digits - and it is still not accurat!

Therefore you try to split a number into a product of a square (the square should be as large as possible) and another rational number. So you are able to calculate the square-root at least from the square. The other number remains under the root sign.

Example:

Since 64 is the greatest square you'll get