If cannot be reduced any further, it is said to be in its basic form. For example, , etc. are surds in its basic forms. Before can be reduced further, “a” must contain a factor which is a perfect square.

Let us take some other surds which are a bit complex such as

 Here, is a surd. Therefore, is also a surd. So, we can say that if any number is in the form of , where is a surd then is also a surd.

Knowing the common square numbers like 4, 9 16, 25, 36, ..., 100 is very helpful when simplifying surd expressions.

Surds can be simplified if the number within the surd has a square number as one of its factors.

Key Point

• When simplifying surds, look for square factors of the number inside the square root and then use