1. Adding and Subtracting Surds
Slideshow 8, Mr Richard Sasaki, Mathematics

2. Objectives
Be able to convert numbers in index form into fractions and surds
Understand the values of surds that cannot be simplified
Be able to add and subtract surds together

3. Index Form Let’s review some rules about index form. 4 1 2 = 4 = ±2=
4 = ±2 =
1 36
6 −2 =
7 7
7 − 1 2 = = =
Writing numbers in surd form can help us simplify them further.

4. Index Form Examples Write 12 1 2 in surd form. 12 1 2 = 12 = 4 ∙ 3 ==
12 =
4 ∙ 3 =
2 3
Write 24 − in surd form.
24 − 1 2 = = = = =
6 12
Just try to remember that 𝑥 = 𝑥 and 𝑥 − 1 2 = 1 𝑥 . If 1 𝑥 is a surd then the denominator must be changed to an integer.

5. Simplifying Surds Surds are often in the form… 𝑎 𝑏 Radicand
𝑎 𝑏
Radicand
If 𝑎 𝑏 is in its simplest form, what values can 𝑏 take? 2, 3, 5, 6, 7,
10, …
These are the numbers that do not have square factors (other than 1).

6. 5
3 2
4 3
21, 22, 23, 26, 29, 30
2 24 45
10 10
1 2
1 9
22 22
2 4
2 8
5 35
5 55 2
4 5
2 3

7. Adding and Subtracting Surds
How can we simplify ?
3 3
If the radicands are the same, we can easily add roots together.
Example
If there are fractions, we need to make the denominators the same too.
Simplify =

8. Adding and Subtracting Surds
Can we simplify ?
No we can’t. Both 3 and 5 are in their simplest forms. So we just leave it the same. =
Example
Simplify
=3∙ ∙2 5 =

9. =3+4=7 but = 25 =5.
∴ 𝑎 + 𝑏 ≠ 𝑎+𝑏
6 3
4 5 −6
11 3
−7 3
3+2 5
30 2 14
6 4
− 17 9
3 8

10. 3 3 −2 5
26 3 −10 13
20 and 2
25 and 2.5
The radicand multiplied by 100 gives the same result multiplied by 10. (i.e if 𝑥 =𝑦, 100𝑥 =10𝑦).
571 =23.9, =239 to 3 s.f each.
3 6
5 5

11. Answers – Part 3
6 6
588 25