We ALWAYS have to leave expressions in the simplest form. Any expression involving a root is called a surd, and we often have to write an answer in surd form which implicitly means simplified surd form:
or
where
are whole numbers or fractions and
and
are as small as possible.
For example:
Simplify
We can write 75 as the product of a number, 3, and a perfect square, 25. Then we take the 25 outside the square root but then we have to square root it:
This is the general procedure. We take out the largest perfect square which is a factor of the number to be rooted. The perfect square can be either a whole number or a fraction.
Example:
Simplify
Example
Simplify
Example: Expand and simplify
Now add up all the terms to obtain