- Rational Number: A number that can be written as a fraction, where both the numerator and the denominator are whole numbers. E.g 3/4
- Irrational Number: They cannot be written as a fraction. They can only be written as decimals numbers. E.g which is equal to 1.7320……
- A surd is a number that’s written with the (under root) sign. Remember the answer has to be irrational.
- Rules for using surds:
Before we move on to surds, let us recall what rational and irrational numbers are.
A rational number is a number that can be written as a fraction, where both the numerator and the denominator are whole numbers.
Every whole number is a rational number, because any whole number can be written as a fraction i.e number 8 is a rational number because it can be written as the fraction 8/1.
Some other examples of rational numbers include:
- 25, 144, 808/56, 103, 492
- 1/2 etc
Numbers that are not rational are considered irrational. Irrational numbers cannot be written as a fraction. They can only be written as decimals numbers.
Moreover, they have endless digits to the right of the decimal point.
Some examples of irrational numbers include:
- The value of which is equal to 3.1415…….
- which is equal to 1.7320……
is not a irrational number as it is equal to 2 ( a whole number).
Now that we have revised what rational and irrational numbers are, let’s move on to Surds.
What are surds?
A surd is a number that’s written with the (under root) sign. It can be a square root , cube root or other n roots.
These are used when an exact answer is required i.e if the answer is , we can leave it like this instead of solving this on a calculator to give an answer in decimals after rounding off like 1.732.
No matter how many decimal places we use, we can never get exactly 3 after squaring 1.7320….. We will end up getting something like 2.99999 which is not very accurate.
Hence, we say that Irrational root of a rational positive number is called a surd. I.e or . Remember the answer has to be irrational, for instance and are not surds as they result in a rational number: and .
Rules for using Surds
Q. Rationalise the denominator of
Firstly multiply the top and bottom by the denominator, but change the sign in front of the surd.
- CGP Edexcel AS-Level Mathematics , Complete Revision and Practice.