√48 can be expressed as the square root of the product of its factors.

So √48 = √(2 x 2 x 2 x 2 x 3) or it can be written √(16 x 3).

If the choice of factors is made such that one (or more) is a perfect square then the square root of that particular factor can be easily obtained leaving only the square root of a reduced number to be obtained.

√48 = √(16 x 3) = √16 x √3 = 4√3

So √48 = √(2 x 2 x 2 x 2 x 3) or it can be written √(16 x 3).

If the choice of factors is made such that one (or more) is a perfect square then the square root of that particular factor can be easily obtained leaving only the square root of a reduced number to be obtained.

√48 = √(16 x 3) = √16 x √3 = 4√3