Surds 3

3.1 Introduction

EMBF

In the previous chapteron exponents, we sawthat rational exponentsare directly related to surds.

We will discuss surds and the laws that governthem further here. While working with surds, always

remember that they aredirectly related to exponents and that you can use your knowledge of one to

help with understandingthe other.

See introductory video:VMebn at http://www.everythingmaths.co.za

3.2 Surd Calculations

There are several laws that make working withsurds (or roots) easier. We will list them all andthen

explain where each rulecomes from in detail.

√nan

√

b =

√n

ab (3.1)

n

�

a

b

=

√na

n√b (3.2)

n√am = amn (3.3)

Surd Law 1:

n

√

a

n

√

b=

n

√

ab EMBH

It is often useful to lookat a surd in exponentialnotation as it allows us to use the exponential laws we

learnt in Grade 10. In exponential notation,n

√

a = a

1

nandn

√

b = b

1

n. Then,

n√an√b = a^1 nb^1 n (3.4)

= (ab)

1

n

=

√n

ab

Some examples using this law:

1.^3

√

16 ×^3

√

4

=^3

√

64

= 4

2.

√

2 ×

√

32

=

√

64

= 8