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Simplifying Surds

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:orwhereare whole numbers or fractions andandare 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