Adding and Subtracting Surds

Adding and Subtracting SurdsSlideshow 8, Mr Richard

Sasaki, Room 307

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

Index FormLet’s review some rules about index form.

√ 4=¿±2162

=¿136

1

712

=¿ 1√7

=¿ Writing numbers in surd form can help us simplify them further.

√77

Index FormExamples

Write in surd form.

√12=¿√ 4 ∙√3=¿2√3 Write in surd form.1

√24=¿√2424

=¿√4 √624

=¿2√62 4

=¿ √612 Just try to remember that and . If is a

surd then the denominator must be changed to an integer.

Simplifying Surds Surds are often in the form… 𝑎√𝑏

Radicand If is in its simplest form, what values can take? 2

, 3,

5,

6,

7,

10, … These are the numbers that do not have square factors (other than 1).

Answers

±5 3√24√3√21 ,√22 ,√23 ,√26 ,√29 ,√30

2√24

√ 45

± 12± 19

√1010

√2222

√24√28

√161161

√535

√555

±24√52√3

(or)

Adding and Subtracting Surds

How can we simplify ? 3√3 If the radicands are the same, we can easily add roots together.ExampleSimplify

4 √62

+ 3√62

=¿7√62

If there are fractions, we need to make the denominators the same too.

Adding and Subtracting Surds

Can we simplify ? No we can’t. Both and are in their simplest forms. So we just leave it the same.

√3+√5=√3+√5ExampleSimplify

3√ 4√3+2√4√5¿3 ∙2√3+2 ∙2√5

¿6 √3+4√5

Answers (Part 1) – Questions 1 to 3

Let .

.

6 √3 4√5 ±6

This is one method… But . .

Answers (Part 1) – Questions 4 - 6

2√3+√511√3

−7 √3

±3+2√530√2

√14

√64

or √38

03√3−2√526 √3−10√13

Answers (Part 2) – Questions 1 - 4 and

and

The radicand multiplied by 100 gives the same result multiplied by 10. (i.e if .

to 3 s.f each.

Answers (Part 2) – Question 5

3√63√32 5√5

√66

4 √33

3√75

29√63

16√29

127√221

127√108

± 58825

7√510