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A surd is the irrational root of a rational number!
We use surds in calculations as they are more accurate than using rounded values.
A topic where we often see values in surd form would be in geometry.
When finding the length of a missing side using Pythagoras’ Theorem, we complete the calculation by taking the square root of a value. If we write the answer to the nearest decimal or whole number, we aren’t left with an exact value. So, using the root of the value gives us an exact answer – even if it is irrational!
Examples of Surds are √2 , √3, √6 ...
We can simplify surds if a factor of the number under the root sign is a square number.
Example 1
Simplify √27
First, we need to see if the value is divisible by a square number.
Listing the square numbers helps with a question such as this.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Looking at the list, 27 is divisible by 9.
We can now re-write the surd as
√(9 x 3)
= √9 x √3
We can simplify now as the square root of 9 is 3
= 3 x √3
Example 2
Simplify √32
Remember that we are looking for a factor pair that has a square number
√32
= √(16 x 2)
= √16 x √2
= 4√2
Let's have a go at some questions now. If you need a reminder of what to do, just click on the red help button on the screen and it will show you this introduction again.
