a a a a
a a n
+ + + + + = ⋅
K
144424443
márte
n
Birdey sanlard kóbeymesin de kópshilik ja®daylarda q-
shamraq jazw menen almastrw maqsetke muwapq bolad.
Tárepini uznl® 5 birlikke te bol®an kvadratt qarayq
(6-súwret). Ol 5 . 5 = 25 birlik kvadrattan ibarat. Tárepini
uznl® 5 birlikke te kub (7-súwret) bolsa 5 . 5 . 5 = 125 birlik
kubt óz ishine alad.
Sizge belgili, 5 . 5 kóbeymesi 5
2
(oqlw: «besti kvadrat»);
5 . 5 . 5 kóbeymesi 5
3
(oqlw: «besti kub») dep belgilenedi:
5 · 5
=
5
2
, 5 · 5 · 5
=
5
3
.
Tap usnday etip, kóbeytiwshileri bir qyl sanlardan ibarat
kóbeymeni ja
a ámel
dárejege kóteriw
menen almastrw
múmkin:
5
3 3 3 3 3 3
+ + + + =
1442443
5 márte
9
1 1 1
1
1
,
7 7 7
7
7
⋅ ⋅ ⋅ ⋅ =
K
144244
3
5 márte
0,4 = (0,4)
1
.
Ulwma, birdey
n
kóbeytiwshilerdi kóbeymesin belgilew
ushn
a
n
jazwnan paydalanlad:
a a a a
a a
⋅ ⋅ ⋅ ⋅ ⋅ =
K
1442443
márte
n
n
III BAP
9-
54
Ol blaynsha oqlad: «
a
sann
n
kórsetkishli dárejesi».
Ádette, qsqasha etip: «
a
n
n
dárejesi» dep aytlad.
a sann n natural kórsetkishli dárejesi dep, hárbiri a ®a te
bol®an n kóbeytiwshini kóbeymesine aytlad:
a
a a a
a
= ⋅ ⋅ ⋅ ⋅
K
14
4244
3
márte
n
n
a
san (tákirarlanwsh kóbeytiwshi)
dárejeni tiykar,
n
san (kóbeytiwshini neshe márte tákirarlanwn kórsetiwshi
san)
dáreje kórsetkishi
dep atalad.
Máselen,
3
4
= 3 · 3 · 3 · 3 = 81,
bul jerde 3 dárejeni tiykar, 4 dáreje kórsetkishi, al 81
bolsa 3
4
dárejesini mánisi.
Tiykarnan, sann birinshi dárejesi dep, us sann ózine
aytlad:
a
1
=
a
.
Máselen,
( )
=
=
=
1
1
1
1
1
7
7
5
5,
25
25,
.
Dárejeni tiykar qálegen san bolw múmkin, máselen,
( )
⋅ ⋅
= ⋅ ⋅ ⋅ ⋅ =
=
=
3
5
2 2 2
8
2
5
5 5 5
125
2
2 2 2 2 2 32;
;
−
= − ⋅ − ⋅ − ⋅ − ⋅ −
= −
5
( 2)
( 2) ( 2) ( 2) ( 2) ( 2)
32;
( ) ( ) ( ) ( ) ( )
−
= −
⋅ −
⋅ −
⋅ −
=
4
2
2
2
2
2
16
3
3
3
3
3
81
;
=
⋅
⋅
=
3
0,2
0,2 0,2 0,2 0,008;
−
= − ⋅ − ⋅ − ⋅ − ⋅ − ⋅ − =
6
( 1)
( 1) ( 1) ( 1) ( 1) ( 1) ( 1) 1;
= ⋅ ⋅ =
=
⋅ ⋅ ⋅
=
3
4
0
0 0 0 0; 10
10 10 10 10 10 000.
6-súwret.
7-súwret.
55
Dárejege kóteriw ámeli úshinshi basqsh ámeli bolad. Eger
a
latpada qawsrmalar bolmasa, onda dáslep úshinshi basqsh
ámeller, keyin ekinshi basqsh ámeller (kóbeytiw hám bóliw)
hám aqrnda, birinshi basqsh ámeller (qosw hám alw)
ornlanatu®nn esletip ótemiz.
Másele.
Esapla
: 7
.
2
4
.
2
7
.
2
4
−
5
.
3
2
= 7
.
16
−
5
.
9 = 112
−
45 = 67.
Sanlard dáreje járdeminde jazwdan kópshilik ja®daylarda,
máselen, natural sanlard ta
ba (razryad) birliklerini qosnds
kórinisinde jazw ushn paydalanlad:
= ⋅
+ ⋅
+ ⋅ + = ⋅
+ ⋅
+ ⋅ +
3
2
.
3245 3 1000 2 100 4 10 5 3 10 2 10
4 10 5
Úlken sanlard jazw ushn kóbinese 10 sann dárejeleri
qollanlad. Máselen, Jerden Quyashqa shekemgi aralq shama
menen 150 mln km ge te bolp, ol 1,5 . 10
8
km kórinisinde
jazlad: Jer sharn radius shama menen 6,37 mln m ge te
,
bul 6,37 . 10
6
m kórinisinde jazlad; Jerden e jaqn juldz®a
(
α
Sentavr) shekemgi aralq 4 . 10
13
km kórinisinde jazlad.
10 nan úlken bol®an hárbir sand
a
.
10
n
kórinisinde
jazw múmkin, bunda 1
≤
a
< 10 hám
n
natural san.
Bunday jazw
sann standart kórinisi
dep atalad.
Máselen,
4578 = 4,578 · 10
3
, 45,78 = 4,578 · 10, 103000 = 1,03 · 10
5
.
Fizika hám ximiya pánlerin úyreniwde, mikrokalkulyatorda
esaplawlarda hám basqa da kópshilik ja®daylarda sann standart
kórinisindegi jazwnan paydalanlad.
Qosndn kóbeyme kórinisinde jaz
(121122):
121.
1)
+ + + +
4 4 4 4 4;
3)
+ +
;
c c c
2)
+ + +
6 6 6 6;
4)
+ + + +
.
a a a a a
S h n ® w l a r
5 3 .
−
56
122.
1)
+
+
2
2
2 ;
m
m
m
5)
3 3
3;
+ + +
K
14243
21 márte
2)
+
+
17
17
17 ;
ab
ab
ab
6)
5 5
5;
+ + +
K
14243
17 márte
3)
−
+ −
(
2 ) (
2 );
c
d
c
d
7)
;
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