The 'perfect square' method is basically saying that see if the number inside the square root is a factor of a perfect square (4, 9, 16, 25, etc). But, square root of 22 is not a factor of one of these, so you just have to approximate this. We known that square root of 25 is 5, and 16 is 4. This has to be between 4 and 5 and a little bit more to the 5 side. So, we can approximately say that:
[tex] \sqrt{22} = 4.71 [/tex]
Hope this helps!
