## Simplifying Surds

We ALWAYS have to leaveexpressions in the simplest form. Any expression involving a root iscalled a surd, and we often have to write an answer in surd formwhich implicitly means simplified surd form:orwherearewhole numbers or fractions andandareas small as possible.

For example:

Simplify

We can write 75 as theproduct of a number, 3, and a perfect square, 25. Then we take the 25outside the square root but then we have to square root it:

This is the generalprocedure. We take out the largest perfect square which is a factorof the number to be rooted. The perfect square can be either a wholenumber or a fraction.

Example:

Simplify

Example

Simplify

Example: Expand andsimplify

Now add up all the terms to obtain