Surds

Surds are used to write irrational numbers precisely.

Leaving the square root sign in is useful for two reasons:

- We don´t need calculators with dealing with them

- They are much more accurate as you don´t have to round off the decimal

Even 1.732050807568877 is not exact. When an answer is required in exact form, you must write it as a surd, ideally simplifying it if possible.

Surds can be simplified if the number in the root symbol has a square number as a factor.

Example: $\sqrt{12}$               Notice that 12 = 4 . 3 

 $3\sqrt{50}$  

50 = 25 . 2  

 $3\sqrt{50}=\sqrt{5\ \ .\ \ 5\ .\ \ 2}=3\sqrt{5^2}.\ \sqrt{2}=3\ .\ 5\ .\ \sqrt{2}=15\sqrt{2}$