Simplify the surd sqrt(48)

When simplifying surd expressions we want to look for square numbers that are factors of the number inside the square root. If we list the square numbers (which are numbers that are the result of squaring another number) up to 48 we have 1, 4, 9, 16, 25 and 36 (1^2, 2^2, ... 6^2). Now we see that 1, 4 and 16 are all factors of 48. Choosing the highest we know that 16 x 3 = 48 so the surd becomes sqrt(16x3). Next, we know that the square root of 16 is 4 so we can apply this and take it outside of the square root giving 4*sqrt(3) (read as 4 root 3). This 4 comes from square rooting 16. As 3 cannot be split up into any more square factors, 4 root 3 is the final answer.