Roots & Radicals
written Fa
th
Def : The there root
of a ,
is
Ura ) = a
such that n 72 will be an
integer ]
"
'
or Ta = a n
n = index , as radicand, F- radical
7th root of a =
exponent & : all exponent laws
apply for roots radicals
( Ta )
m
( a"ntm= a' amin Fam
Eg
mm
: = = =
N . B : When n =L ,
the index is suppressed (square root) :Ña=ra
* Properties :
1- nra .
V6 = #
Eg : Too
"
2
.
3
V27
'
6
= 78.27 cannot be combined
I
" such
=
152.521
.
NB : The index n must be the same
2. =
Fair
far
addition / subtraction w/ radicals we
*
the similar terms
may
i. e , the terms w/ the same index
combine ,
only
,
& the same radicand .
252 t 352 1- 253 1- 3D 1- P2
Eg : -
= 5 ra t 553 1- T2 ( cannot combine w/ different index)
-
252 t 208 (different radicand)
A. 8 : sometimes we can
simplify a
square root by writing
the radicand as a
product of a nb & a perfect
square
s drat 254.2 = 252 1-
= 2K€ = 2521-2.252
= 252 + 4r2 = 652
-
R2 = RES = ru V3 = 253
-
R2 = T2 = F ra
written Fa
th
Def : The there root
of a ,
is
Ura ) = a
such that n 72 will be an
integer ]
"
'
or Ta = a n
n = index , as radicand, F- radical
7th root of a =
exponent & : all exponent laws
apply for roots radicals
( Ta )
m
( a"ntm= a' amin Fam
Eg
mm
: = = =
N . B : When n =L ,
the index is suppressed (square root) :Ña=ra
* Properties :
1- nra .
V6 = #
Eg : Too
"
2
.
3
V27
'
6
= 78.27 cannot be combined
I
" such
=
152.521
.
NB : The index n must be the same
2. =
Fair
far
addition / subtraction w/ radicals we
*
the similar terms
may
i. e , the terms w/ the same index
combine ,
only
,
& the same radicand .
252 t 352 1- 253 1- 3D 1- P2
Eg : -
= 5 ra t 553 1- T2 ( cannot combine w/ different index)
-
252 t 208 (different radicand)
A. 8 : sometimes we can
simplify a
square root by writing
the radicand as a
product of a nb & a perfect
square
s drat 254.2 = 252 1-
= 2K€ = 2521-2.252
= 252 + 4r2 = 652
-
R2 = RES = ru V3 = 253
-
R2 = T2 = F ra
