Repeated multiplication Can represents

into a

a
power axaxa
IIaxiinmesan

II
owers as whole

we pay

axa a a f

Reads as

staff

Third

power

Read as
I as

Mad

a
cube of

a aberoot of 4

axexa as

exit

at a as

EP

s
ants ab

95 3
as

5
F

amn am anthram


s
Fa

a s

ax's sat

Mn am't

Nam

a I

Fx

fractional indices also known

as Surds

sards has no
exactly

Sundsarenotd

EI not possible

242 I is

to write into a rational number

Bar a o


Surds are also known as irrational numbers

Irrational numbers are nonterminating numbers

Irrational numbers are Non-recurring decimals

Irrational numbers or surds

and mom
recurring
non

are

terminating decimals

These numbers can not expressed

form of Pyg

in the

rational irrational number

numby sards

not in

1 Are in Are perform

Pg tops

940

Are non terminals

Are recurring

and non
recurring

terminating

decimals

decimals

not defined
3

defined
denoted by

4 denoted by
g

Part of Surds

corderoffund

Fa tf the 3rd

Ert at 57 35 35

radicand and index

Ifa power of

value

teen
given

are equal

deined not defined

at g

3
of

Ex Ta Last a

2
5

93 se

Say 53 53 B I 3

as 355 a 355 X 355 53

1. The reverse of squaring a number is finding its

2. Squaring either a positive or negative real number yields a positive result.

(True / False)

3.A square root of a number is one of two e__________ of that number.

5.Every positive real number has ____________how many square roots

6.The symbol V is called the r____________ sign

7.The two square roots of a number are equal in a _______________. _ but

opposite in sign.

8.The number under the radical sign is called the______________

9.The combination of the radical sign together with the number under it is called the

r_____________

10. The square root of a rational number is always rational. (True / False)

Raising “a” to the power “m” is indicated by the expression

Similarly, extracting

the root of a is indicated by

The symbol V is called the radical sign,

a is termed the radicand, and m is known as the index.

If no index is written, it is assumed to be 2,

means the positive square root of a.

A square root of a (indicated by

ra ) is one of two equal factors of a.

A cube root of a (indicated by ) is one of three equal factors of a.

Ja

A fourth root of a (indicated by ) is one of four equal factors of a.

ta

A number is an root of a given number if it is one of the n equal factors of that

number.

What are the factors of a On and

me as a
ah ah

What are the two equal factors of a

ab ab ab
.

What are the three equal factors of a

ab y 13 x a d

What are the “n” equal factors

jam of a

a im

at t t
t n time an

t
at

Similar radicals or similar Surds

1.To simplify a radical, it is always in simplest form

2.Similar radicals have the same index and the same
radicand.
3.Similar radicals may be combined by addition and
subtraction

B 53 0

A a O

a 253 153 B
2 a a

1553

253 353

5A 29 39

not possible to simplify

a b

possible to Simplify

not

V3 56
To add or to subtract you need similar surds

Similar surds

These are monomial surds, with same index and same

radicand

Coe cient may di er

Set I 7 55 355 1055

55 753,1053

Set I 5 4

Set II a

set I 5 Ft

MULTIPLYING AND DIVIDING RADICALS

1. The product of two or more square roots is gives another

square root..

2. The product of two or more cube roots is gives another cube root.

3.If radicals have same index, then they are multiplied or divided by
themselves.

Simplifying radical( Surds)Equations

(1) Rearrange the terms of the equation

(2) Isolate the variable ,which is in the radical form
(3) Square both sides.
(4) Solve for the unknown or variable
In a fraction if the denominator is under square root
Then multiply both the numerator and the denominator
by a number that will make the denominator a perfect
square.

This procedure, known as rationalising the

denominator.


form of surds

Simplest P
SE

Mr UR 23 8
35

F8 Fxs 352
221

256

Fy FG

stg Ey 58 3

3533 255

Ps4 FAT

3 55
TIL
A2
3 52

355

TEXT

. 399 far

FEE a'dos
 53 0
a a o

a 253 153 53
2 a a f

553 253 353

5A 29 39

a b not possible to simplify

not possible to Simplify

V3 56

To Add on To subtract you

need Simalar Surds

Similssamerdsdex and same

radicand
V5 55 355 A
557 355 7 353
1053 5Th 1055
 Set I 55
355 index 21
5
1055 radicand

Set I 353
index 3
753
1053 radicand 3

MULTIPLYING AND DIVIDING RADICALS

1. The product of two or more square roots is gives another square root..

2.The product of two or more cube roots is gives another cube root

3.If radicals have same index, then they are multiplied or divided by
themselves