Facts about Rational Numbers

• can be a whole number

• can be a fraction

• can be an integer

• can be a ratio

• can be a repeating decimal

• can be a terminating decimal

• can be a perfect square

Facts about Irrational Numbers

• cannot be written as a fraction or ratio

• non terminating decimal

• non repeating decimal

• non perfect squares

A surd is an expression that includes a square root, cube root or other root symbol.

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

This answer is in surd form. It is irrational and it is said to be "in exact form". A decimal answer, such as 1.73 (2 decimal places), is not exact.

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.

The following rules apply:

​These are corollaries of the laws of indices

Examples:

Simplifying surds:

Another example: