1. Millburn Academy
Maths department
National 5
Surds 1

2. A surd is an irrational number, which is the root (square, cube etc) of another number.
Examples:
2 =
1∙ ….
so 2 is a surd
3 =
1∙ ….
so 3 is a surd
4 = 2
so 4 is NOT a surd
3 5 =
1∙ ….
so is a surd

3. We can add or subtract surds of the same value.
Examples: =
2× 3
or 2 3 =
9 2
10 7 −6 7 =
4 7
−6 5 =
10 5

4. Simplifying Surds
8 is a surd
but it can be simplified
We can simplify a surd if it can be divided by a square number.
Reminder:
Square Numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 ….
8 =
4 × 2
=2 × 2
=2 2

5. Simplifying the following surds:
1) 45 =
9 × 5
3) 80 =
16 × 5
=3 5
=4 5
2) 75 =
25 × 3
4) =
100 × 7
=5 3
=10 7

6. These surds are different so can’t be added together.5) =
However can be simplified. =
=3 3
We can now add them together.
6) 98 − 32
= 49 × 2 − 16 × 2
=7 2 −4 2
=3 2