Exponents and Square Roots
A square root goes the other way:
1 1
2
2 4
2
3
1 1
The
2 exponent of a number says how
3
 times
9 to use the number in a
many
2
multiplication.
4
 16
In 32 the "2" says to use 3 twice in a
multiplication,
52 2 25
so 3 = “3 to the 2nd power”
6 2  36
or “3 squared” = 3 × 3= 64
7 2  49
82  64
Perfect
922 181
1
Squares
22
10
2 4100
2
1 1
2
11
3222 94121
22
12
144
2 16
4
3 9
2
13
169
5422 16
25
22
14
196
2 36
6
5  25
2
15
225
76 22 
36
49
2
16
256
8722 64
49
2 2  289
17
 81
892 
64
18
324
10
100
9 2 81
22
19
361
11
10 2  121
100
22
20 121
400
12
144
11
21222 
 169
441
13
12
144
22
2
22222 
484
14
 169
196
13
222
23
529
15
225
14 
 196
24222 
576
16
 225
256
15
25222 
625
17
 256
289
16
2
18
17 2
2
19
182

 324
289
 324
361

Translation
1 squared is 1
2 squared is 4
3 squared is 9
4 squared is 16
42
9 3
Radical sign (or
square root sign)
9
Radicand
is 9, so a square root of 9 is 3
163squared
4
A square root of a number is a value that can be
multiplied
25  5 by itself to give the original number.
9 = a square root of 9 is 3,
36 when
6 3 is multiplied by itself you get 9.
because
It is like asking: What can I multiply by itself to get
49  7
this?
64  8
1811 9
Square Roots
100
14 12 10
94 
121
 3
2 11
16
144
9 3412
25 4513
169
16
Translation
The square root of 1 is 1
The square root of 4 is 2
The square root of 9 is 3
The square root of 16 is 4
6 squared is 26
36
196
25 
6514
49 
6715
225
36
7 squared is 49
64
256
49 
8716
The square root of 49 is 7
8 squared is 64
81
2899817
64
The square root of 64 is 8
5 squared is 25
The square root of 25 is 5
The square root of 36 is 6
10 squared is 100
100
324910
18
81
121
361  11
19
100
10
11 squared is 121
144
12
400 11
20
121
The square root of 121 is 11
12 squared is 144
169
441 
21
144
 13
12
The square root of 144 is 12
9 squared is 81
13 squared is 169
15 squared is 225
16 squared is 256
25 squared is 625
196
484 
22
169
 14
13
225  14
15
529
23
196
256
576
225
289
625
256
 15
16
24


25
 17
16
324
289 
 18
17
361
324  19
18
The square root of 81 is 9
The square root of 100 is 10
The square root of 169 is 13
The square root of 225 is 15
The square root of 256 is 16
The square root of 625 is 25
EXPONENTS
2
3 is an example of EXPONENTIAL NOTATION. The small-sized number is the exponent, and the large-sized
number is the base. The exponent determines how many times the base is repeated to make a product.
2
3 means 3 is the base and 2 is the exponent, so it can be rewritten as 3x3, which is 9.
3
2 means 2 is the base and 3 is the exponent, so it can be rewritten as 2x2x2, which is 8.
Expand each notation and find its value.
1. 54 = ________=____
2. 121 = _____=____
3. 105 = _________ = ___
Express each number as a power of 10.
4. 1,000,000 = ______
5. 10,000 = ______
Rewrite each number as product of a power of 10 as one of the factors.
6. 600 = ____________
7. 5,300,000 = _____________
8. 70 = ____________
9. 23,100 = ___________