MATEMATIKA
Úvod
Číselné obory
Číselné obory - př.
Poměr a úměra
Procenta
Množiny
základní pojmy
intervaly
absolutní hodnota čísla
Logika
výroky
kvantifikované výroky
Mocniny
a odmocniny
mocniny s přirozeným exponentem
mocniny s celočíselným exponentem
mocniny s racionálním exponentem
n-tá odmocnina
početní výkony s odmocninami
zápis čísla ve tvaru a.10
n
Algebraické výrazy
výrazy a mnohočleny
úpravy výrazů
lomené výrazy
Funkce
vlastnosti
lineární
kvadratické
mocninné
exponenciální
logaritmické
Rovnice
lineární
kvadratické
iracionální
exponenciální
goniometrické
logaritmus
logaritmické rovnice
Nerovnice
lineární
kvadratické
exponenciální
logaritmické
Soustavy rovnic
a nerovnic
Soustavy lineárních rovnic
Soustavy lineárních a kvadratických rovnic
Goniometrie
goniometrické funkce
Planimetrie
shodnost a podobnost trojúhelníků
Euklidovy věty
rovinné obrazce
Trigonometrie
pravoúhlý trojúhelník
obecný trojúhelník
Komplexní čísla
algebraický tvar
goniometrický tvar
Moivreova věta
kvadratické rovnice v oboru C
Posloupnosti
aritmetická posloupnost
geometrická posloupnost
Analytická
geometrie v rovině
vektory
přímka
vzájemná poloha přímek a bodů
kružnice
elipsa
parabola
hyperbola
Kombinatorika
Variace
Permutace
Kombinace
Kombinační čísla a jejich vlastnosti
Binomická věta
Pravděpodobnost
příklady
Aplikace matematiky
bankovnictví
investice
statistika
Početní výkony s odmocninami - příklady
Částečné odmocnění
Příklad 1
Částečně odmocni:
12
2
⋅
3
50
5
⋅
2
72
6
⋅
2
44
2
⋅
11
98
7
⋅
2
48
4
⋅
3
600
10
⋅
6
240
4
⋅
15
162
9
⋅
2
Řešení
12
=
4
⋅
3
=
4
⋅
3
=
2
⋅
3
50
=
25
⋅
2
=
25
⋅
2
=
5
⋅
2
72
=
36
⋅
2
=
36
⋅
2
=
6
⋅
2
44
=
4
⋅
11
=
4
⋅
11
=
2
⋅
11
98
=
49
⋅
2
=
49
⋅
2
=
7
⋅
2
48
=
16
⋅
3
=
16
⋅
3
=
4
⋅
3
600
=
100
⋅
6
=
100
⋅
6
=
10
⋅
6
240
=
16
⋅
15
=
16
⋅
15
=
4
⋅
15
162
=
81
⋅
2
=
81
⋅
2
=
9
⋅
2
Příklad 2
Částečně odmocni:
4
a
5
b
3
2
a
2
b
a
b
121
m
5
11
m
2
m
9
a
3
b
3
a
a
b
x
0
y
3
64
y
⋅
y
8
40
a
9
b
5
2
a
4
b
2
10
a
b
147
s
41
4
k
8
7
s
20
3
s
2
k
4
27
a
9
b
11
c
21
3
a
4
b
5
c
10
3
a
b
c
Řešení
4
a
5
b
3
=
=
4
⋅
a
4
⋅
a
⋅
b
2
⋅
b
=
=
2
a
2
b
a
b
121
m
5
=
=
121
⋅
m
4
⋅
m
=
=
11
m
2
m
9
a
3
b
=
=
9
⋅
a
2
⋅
a
⋅
b
=
=
3
a
a
b
x
0
y
3
64
=
=
1
⋅
y
2
⋅
y
64
=
=
y
⋅
y
8
40
a
9
b
5
=
=
4
⋅
10
⋅
a
8
⋅
a
⋅
b
4
⋅
b
=
=
2
a
4
b
2
10
a
b
147
s
41
4
k
8
=
=
147
⋅
s
41
4
⋅
k
8
=
=
49
⋅
3
⋅
s
40
⋅
s
2
k
4
=
=
7
s
20
3
s
2
k
4
27
a
9
b
11
c
21
=
=
9
⋅
3
⋅
a
8
⋅
a
⋅
b
10
⋅
b
⋅
c
20
⋅
c
=
=
3
⋅
3
⋅
a
4
⋅
a
⋅
b
5
⋅
b
⋅
c
10
⋅
c
=
=
3
a
4
b
5
c
10
3
a
b
c
Příklad 3
Částečně odmocni:
48
3
2
⋅
6
3
2
000
3
10
⋅
2
3
128
3
4
⋅
2
3
40
3
2
⋅
5
3
162
3
3
⋅
2
4
32
3
2
⋅
4
3
81
3
3
⋅
3
3
Řešení
48
3
=
2
3
⋅
6
3
=
2
⋅
6
3
2
000
3
=
1
000
⋅
2
3
=
10
⋅
2
3
128
3
=
2
6
⋅
2
3
=
2
2
⋅
2
3
=
4
⋅
2
3
40
3
=
8
⋅
5
3
=
2
3
⋅
5
3
=
2
⋅
5
3
162
4
=
27
⋅
6
4
=
3
4
⋅
2
4
=
3
⋅
2
4
32
3
=
2
3
⋅
2
2
3
=
2
⋅
4
3
81
3
=
3
3
⋅
3
3
=
3
⋅
3
3
Příklad 4
Částečně odmocni:
a
7
5
a
⋅
a
2
5
50
b
2
⋅
b
7
10
8
a
7
b
8
3
2
a
2
b
2
⋅
a
b
2
3
8
13
6
64
⋅
2
a
b
10
3
b
3
⋅
a
b
3
k
6
y
10
5
k
⋅
k
5
y
2
a
13
b
10
1
024
10
a
b
⋅
a
3
10
2
8
7
a
13
b
11
6
8
a
2
b
⋅
8
a
b
5
6
a
8
b
12
32
c
5
5
a
b
2
⋅
a
3
b
2
5
2
c
Řešení
a
7
5
=
a
5
⋅
a
2
5
=
a
⋅
a
2
5
b
27
10
=
b
20
⋅
b
7
10
=
b
2
⋅
b
7
10
8
a
7
b
8
3
=
2
3
⋅
a
6
⋅
a
⋅
b
6
⋅
b
2
3
=
2
a
2
b
2
⋅
a
b
2
3
8
13
6
=
8
12
⋅
8
6
=
64
⋅
8
6
=
64
⋅
2
3
6
=
64
⋅
2
a
b
10
3
=
a
⋅
b
9
⋅
b
3
=
b
3
⋅
a
b
3
k
6
y
10
5
=
k
5
⋅
k
5
y
10
5
=
k
⋅
k
5
y
2
a
13
b
10
1
024
10
=
a
10
⋅
a
3
⋅
b
10
10
2
10
10
=
a
b
⋅
a
3
10
2
8
7
a
13
b
11
6
=
8
6
⋅
8
⋅
a
12
⋅
a
⋅
b
6
⋅
b
5
6
=
8
a
2
b
⋅
8
a
b
5
6
a
8
b
12
32
c
5
5
=
a
5
⋅
a
3
⋅
b
10
⋅
b
2
5
2
5
⋅
c
5
5
=
a
b
2
⋅
a
3
b
2
5
2
c
Příklad 5
S použitím částečného odmocnění vypočítej:
8
44
−
6
99
−
2
11
12
−
48
+
2
75
8
3
(
−
5
2
+
3
50
)
−
18
7
2
7
20
−
5
45
−
5
8
50
−
4
32
−
6
162
2
2
−
4
216
−
12
150
−
84
6
98
+
200
+
128
25
2
300
−
(
75
+
108
)
−
3
2
108
−
2
27
+
12
12
30
3
Řešení
8
44
−
6
99
=
8
4
⋅
11
−
6
9
⋅
11
=
16
11
−
18
11
=
−
2
11
12
−
48
+
2
75
=
4
⋅
3
−
16
⋅
3
+
2
25
⋅
3
=
2
3
−
4
3
+
10
3
=
=
8
3
(
−
5
2
+
3
50
)
−
18
=
(
−
5
2
+
3
25
⋅
2
)
−
9
⋅
2
=
=
(
−
5
2
+
15
2
)
−
3
2
=
10
2
−
3
2
=
7
2
7
20
−
5
45
=
7
4
⋅
5
−
5
9
⋅
5
=
14
5
−
15
5
=
−
5
8
50
+
4
32
−
6
162
=
8
25
⋅
2
+
4
16
⋅
2
−
6
81
⋅
2
=
=
40
2
+
16
2
−
54
2
=
2
2
−
4
216
−
12
150
=
−
4
36
⋅
6
−
12
25
⋅
6
=
−
24
6
−
60
6
=
−
84
6
98
+
200
+
128
=
49
⋅
2
+
100
⋅
2
+
64
⋅
2
=
=
7
2
+
10
2
+
8
2
=
25
2
300
−
(
75
+
108
)
=
100
⋅
3
−
(
25
⋅
3
+
36
⋅
3
)
=
=
10
3
−
(
5
3
+
6
3
)
=
10
3
−
11
3
=
−
3
2
108
−
2
27
+
12
12
=
2
36
⋅
3
−
2
9
⋅
3
+
12
4
⋅
3
=
=
12
3
−
6
3
+
24
3
=
30
3
Příklad 6
S použitím částečného odmocnění vypočítej:
3
4
000
3
−
32
3
28
⋅
4
3
16
3
−
54
3
+
2
⋅
250
3
9
⋅
2
3
11
⋅
48
3
−
750
3
17
⋅
6
3
128
3
+
2
⋅
16
3
−
1
024
3
0
4
a
⋅
16
a
2
b
7
3
−
7
b
⋅
250
a
5
b
4
3
−
27
a
b
2
⋅
2
a
2
b
3
405
4
+
3
⋅
80
4
−
5
⋅
5
4
4
⋅
5
4
Řešení
3
⋅
4
000
3
−
32
3
=
3
⋅
1
000
⋅
4
3
−
8
⋅
4
3
=
30
⋅
4
3
−
2
⋅
4
3
=
28
⋅
4
3
16
3
−
54
3
+
2
⋅
250
3
=
8
⋅
2
3
−
27
⋅
2
3
+
2
⋅
125
⋅
2
3
=
=
2
⋅
2
3
−
3
⋅
2
3
+
10
⋅
2
3
=
9
⋅
2
3
11
⋅
48
3
−
750
3
=
11
⋅
8
⋅
6
3
−
125
⋅
6
3
=
22
⋅
6
3
−
5
⋅
6
3
=
17
⋅
6
3
128
3
+
2
⋅
16
3
−
1
024
3
=
64
⋅
2
3
+
2
⋅
8
⋅
2
3
−
512
⋅
2
3
=
=
4
2
3
+
4
⋅
2
3
−
8
⋅
2
3
=
0
4
a
⋅
16
a
2
b
7
3
−
7
b
⋅
250
a
5
b
4
3
=
=
4
a
⋅
8
⋅
2
⋅
a
2
⋅
b
6
⋅
b
3
−
7
b
⋅
125
⋅
2
⋅
a
3
⋅
a
2
⋅
b
3
⋅
b
3
=
=
8
a
b
2
⋅
2
a
2
b
3
−
35
a
b
2
⋅
2
a
2
b
3
=
−
27
a
b
2
⋅
2
a
2
b
3
405
4
+
3
⋅
80
4
−
5
⋅
5
4
=
81
⋅
5
4
+
3
⋅
16
⋅
5
4
−
5
⋅
5
4
=
=
3
⋅
5
4
+
6
⋅
5
4
−
5
⋅
5
4
=
4
⋅
5
4
Usměrňování zlomků
Příklad 1
Usměrni zlomky:
1
2
2
2
−
6
6
−
6
3
5
15
5
9
5
3
3
3
5
4
2
3
5
4
10
15
−
26
3
13
−
2
13
3
6
−
12
3
2
3
3
12
6
2
6
2
+
3
5
2
5
+
15
5
a
−
b
a
a
−
b
a
a
4
15
+
5
12
2
3
2
5
+
5
Řešení
1
2
=
=
1
2
⋅
2
2
=
=
2
2
−
6
6
=
=
−
6
6
⋅
6
6
=
=
−
6
6
6
=
=
−
6
3
5
=
=
3
5
⋅
5
5
=
=
15
5
9
5
3
=
=
9
5
3
⋅
3
3
=
=
9
3
15
=
=
3
3
5
4
2
3
5
=
=
4
2
3
5
⋅
5
5
=
=
4
10
15
−
26
3
13
=
=
−
26
3
13
⋅
13
13
=
=
−
26
13
39
=
=
−
2
13
3
6
−
12
3
=
=
6
−
12
3
⋅
3
3
=
=
6
3
−
48
3
=
=
6
3
−
16
⋅
3
3
=
=
6
3
−
4
3
3
=
=
2
3
3
12
6
=
=
12
6
⋅
6
6
=
=
12
6
6
=
=
2
6
2
+
3
5
=
=
2
+
3
5
⋅
5
5
=
=
2
5
+
15
5
a
−
b
a
=
=
a
−
b
a
⋅
a
a
=
=
a
−
b
a
a
4
15
+
5
12
2
3
=
=
4
15
+
5
12
2
3
⋅
3
3
=
=
4
45
+
5
36
2
⋅
3
=
=
4
9
⋅
5
+
5
⋅
6
6
=
=
4
⋅
3
5
+
30
6
=
=
12
5
+
30
6
=
=
6
(
2
5
+
5
)
6
=
=
2
5
+
5
Příklad 2
Usměrni zlomky:
3
3
+
2
3
(
3
−
2
)
14
1
−
2
2
−
2
−
4
2
5
−
3
5
+
3
14
−
5
3
11
2
3
+
2
2
2
−
3
2
+
6
19
6
5
3
+
3
2
5
2
−
2
3
2
3
−
10
6
−
5
2
3
5
−
5
3
3
5
+
5
3
15
−
4
a
a
−
b
a
(
a
+
b
)
a
−
b
Řešení
3
3
+
2
=
=
3
3
+
2
⋅
3
−
2
3
−
2
=
=
3
(
3
−
2
)
3
−
2
=
=
3
(
3
−
2
)
14
1
−
2
2
=
=
14
1
−
2
2
⋅
1
+
2
2
1
+
2
2
=
=
14
(
1
+
2
2
)
1
−
4
⋅
2
=
=
14
(
1
+
2
2
)
−
7
=
=
−
2
−
4
2
5
−
3
5
+
3
=
=
5
−
3
5
+
3
⋅
5
−
3
5
−
3
=
=
(
5
−
3
)
2
25
−
3
=
=
25
−
10
3
+
3
22
=
=
28
−
10
3
22
=
=
2
(
14
−
5
3
)
22
=
=
14
−
5
3
11
2
3
+
2
2
2
−
3
=
=
2
3
+
2
2
2
−
3
⋅
2
2
+
3
2
2
+
3
=
=
(
2
3
+
2
)
⋅
(
2
2
+
3
)
4
⋅
2
−
3
=
=
4
6
+
2
9
+
2
4
+
6
5
=
=
5
6
+
6
+
4
5
=
=
10
+
5
6
5
=
=
5
(
2
+
6
)
5
=
=
2
+
6
19
6
5
3
+
3
2
=
=
19
6
5
3
+
3
2
⋅
5
3
−
3
2
5
3
−
3
2
=
=
19
6
(
5
3
−
3
2
)
25
⋅
3
−
9
⋅
2
=
=
95
18
−
57
12
57
=
=
95
9
⋅
2
−
57
4
⋅
3
57
=
=
285
2
−
114
3
57
=
=
57
(
5
2
−
2
3
)
57
=
=
5
2
−
2
3
2
3
−
10
6
−
5
=
=
2
3
−
10
6
−
5
⋅
6
+
5
6
+
5
=
=
(
2
3
−
10
)
(
6
+
5
)
6
−
5
=
=
2
18
+
2
15
−
60
−
50
=
=
2
9
⋅
2
+
2
15
−
4
⋅
15
−
25
⋅
2
=
=
6
2
+
2
15
−
2
15
−
5
2
=
=
2
3
5
−
5
3
3
5
+
5
3
=
=
3
5
−
5
3
3
5
+
5
3
⋅
3
5
−
5
3
3
5
−
5
3
=
=
(
3
5
−
5
3
)
2
9
⋅
5
−
25
⋅
3
=
=
9
⋅
5
−
30
15
+
25
⋅
3
−
30
=
=
120
−
30
15
−
30
=
=
15
−
4
a
a
−
b
=
=
a
a
−
b
⋅
a
+
b
a
+
b
=
=
a
(
a
+
b
)
a
−
b
Příklad 3
Usměrni zlomky:
1
+
2
+
3
1
+
2
−
3
3
2
+
2
+
6
+
2
3
2
2
3
3
2
9
3
3
2
z
z
5
7
2
z
2
7
1
10
3
4
10
4
10
7
x
3
x
9
4
7
x
3
4
1
32
3
2
3
4
Řešení
1
+
2
+
3
1
+
2
−
3
=
(
1
+
2
)
+
3
(
1
+
2
)
−
3
⋅
(
1
+
2
)
+
3
(
1
+
2
)
+
3
=
=
[
(
1
+
2
)
+
3
]
2
(
1
+
2
)
2
−
3
=
(
1
+
2
)
2
+
2
3
(
1
+
2
)
+
3
1
+
2
2
+
2
−
3
=
=
1
+
2
2
+
2
+
2
3
+
2
6
+
3
2
2
=
6
+
2
2
+
2
3
+
2
6
2
2
=
=
6
+
2
2
+
2
3
+
2
6
2
2
⋅
2
2
=
6
2
+
2
4
+
2
6
+
2
12
2
4
=
=
6
2
+
2
⋅
2
+
2
6
+
2
4
⋅
3
4
=
6
2
+
4
+
2
6
+
4
3
4
=
=
3
2
+
2
+
6
+
2
3
2
2
3
3
=
2
3
3
⋅
3
2
3
3
2
3
=
2
9
3
3
3
3
=
2
9
3
3
2
z
z
5
7
=
2
z
z
5
7
⋅
z
2
7
z
2
7
=
2
z
z
2
7
z
7
7
=
2
z
z
2
7
z
=
2
z
2
7
1
10
3
4
=
1
10
3
4
⋅
10
4
10
4
=
10
4
10
4
4
=
10
4
10
7
x
3
x
9
4
=
7
x
3
x
8
⋅
x
4
=
7
x
3
x
2
⋅
x
4
⋅
x
3
4
x
3
4
=
7
x
3
⋅
x
3
4
x
2
⋅
x
4
4
=
7
x
3
⋅
x
3
4
x
3
=
7
x
3
4
1
32
3
=
1
2
5
3
=
1
2
3
⋅
2
2
3
=
1
2
⋅
2
2
3
⋅
2
3
2
3
=
2
3
2
⋅
2
=
2
3
4
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