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EC
Gr6-C4: Squares and Square Roots
ExpertChild
Name:
Date:
Start Time:
A+
0
Grade:
Number of mistakes:
:
End Time:
A
1
B
2-3
C
4-6
:
D
7+
Math Concept
A square is the product of a number and itself.
Example:
3×3=9
⇒ 9 is the square of 3
6 × 6 = 36
⇒ 36 is the square of 6
Find the square of the following numbers.
[1]
square of 8 =
8×8
[2]
square of 5 =
×
[3]
square of 1 =
= 64
=
=
[4]
square of 7 =
=
[5]
square of 0 =
=
[6]
square of 6 =
=
Math Concept
The square root of a number is one of the equal factors of the number. The square root
is the inverse of square.
Example:
64 = 8 × 8
⇒ 8 is the square root of 64
25 = 5 × 5
⇒ 5 is the square root of 25
Find the equal factors and the square root.
[7]
36 =
6×6
square root of 36 =
[8]
81 =
[10]
6
×
square root of 4 =
[11]
square root of 81 =
[9]
9=
×
square root of 9 =
Copyright  2009 by ExpertChild Inc.
4=
25 =
square root of 25 =
[12]
16 =
square root of 16 =
1
EC
Gr6-C4: Squares and Square Roots
ExpertChild
Math Concept
Square roots are written with the symbol
Example:
36 = square root of 36 = 6
.
(note, 36 = 6 × 6)
Find the equal factors and the square root.
[1]
25 = square root of 25 = 5
[10]
100 =
[2]
81 = square root of 81 =
[11]
144 =
[3]
121 =
[12]
400 =
[4]
49 =
[13]
1600 =
[5]
0 =
[14]
1 =
[6]
64 =
[15]
16 =
[7]
0.25 =
[16]
0.81 =
[8]
0.16 =
[17]
0.64 =
[9]
0.49 =
[18]
0.36 =
(0.25 = 0.5 × 0.5)
Copyright  2009 by ExpertChild Inc.
2
EC
Gr6-C4: Squares and Square Roots
ExpertChild
Prime and Composite Numbers
Math Concept
A number that can be divided only by 1 and the number itself is called a prime number.
A number that is not a prime number is a composite number.
5 can be divided only by 1 and 5. So, 5 is a prime number. 12 can be divided by 1,
2, 3, 6 and 12. So, 12 is not a prime number and is a composite number.
The 1-digit prime numbers are 2, 3, 5, and 7.
The 1-digit composite numbers ate 4, 6, 8, and 9.
1 is neither a prime number nor a composite number.
Circle the prime number.
[1]
1
7
15
[5]
3
75
100
[2]
18
23
30
[6]
21
1
5
[3]
11
33
27
[7]
35
54
13
[4]
86
25
2
[8]
19
10
8
Circle the composite number.
[9]
2
5
75
[13]
70
7
11
[10]
13
62
19
[14]
11
12
13
[11]
7
23
34
[15]
1
19
20
[12]
11
18
1
[16]
5
14
11
[17]
Write first 6 prime numbers.
2 ,
[18]
3 , ____, ____, ____, ____
Write first 6 composite numbers.
4 ,
6 , ____, ____, ____, ____
Copyright  2009 by ExpertChild Inc.
3
EC
Gr6-C4: Squares and Square Roots
ExpertChild
Prime Factorization
Math Concept
If a number is written as the product of only prime numbers, we get the prime
factorization of the number.
All the factors in 20 = 2 × 2 × 5 are prime numbers. So, it is the prime
factorization of 20.
One of the factors in 20 = 2 × 10 is not a prime numbers (since 10 = 2 × 5,
10 is not a prime number). So, 2 × 10 is not the prime factorization of 20.
Find the prime factors of the following numbers.
Note:
[1]
While selecting the divisor, use divisor 2 as long as the quotient is even. When the quotient
becomes odd, try the divisors 3, 5, 7, 11, 13, 17, 19, etc., which are all prime numbers.
2 60
(60 ÷ 2 = 30)
Step-1: Divide the number by a prime number.
2 30
(30 ÷ 2 = 15)
3 15
Step-2: If the quotient is not 1, divide the quotient by
a prime number.
(15 ÷ 3 = 5)
5
(5 ÷ 5 = 1)
5
Prime factors of 60 = 2 × 2 × 3 × 5
1
[2]
Step-3: Continue this process till the quotient
becomes 1.
150 = ____________________
[4]
64 = _____________________
[5]
48 = _____________________
150
[3]
36 = _____________________
Copyright  2009 by ExpertChild Inc.
4
EC
Gr6-C4: Squares and Square Roots
ExpertChild
Find Square Root using Prime Factorization
Find the square root of the following numbers.
[1]
2 36
(36 ÷ 2 = 18)
2 18
(18 ÷ 2 = 9)
3 9
(9 ÷ 3 = 3)
3 3
(3 ÷ 3 = 1)
1
[2]
Step-1: Find the prime factors of 36.
Prime factors of 36 = 2 × 2 × 3 × 3
Step-2: Group the prime factors into two groups so
that factors in both the groups are same
36 = (2 × 3) × (2 × 3)
=6×6
Step-3: So,
100 = 2 × 2 × 5 × 5 = (2 × 5) × (2 × 5)
[5]
36 = 6
64 = _____________________
2 100
2 50
5 25
5
100 = 2 × 5 = 10
[3]
225 = _____________________
64 = _____
[6]
225 = ______
[4]
625 = _____________________
625 = ______
Copyright  2009 by ExpertChild Inc.
196 = _____________________
196 = ______
[7]
144 = _____________________
144 = ______
5
EC
Gr6-C4: Squares and Square Roots
ExpertChild
Find the square root of the following numbers.
Note:
[1]
While selecting the divisor, use smallest possible whole number or decimal as the divisor.
3 0.81
(0.81 ÷ 3 = 0.27)
3 0.27
(0.27 ÷ 3 = 0.09)
0.3 0.09
(0.09 ÷ 0.3 = 0.3)
0.3
Step-1: 0.81 = 3 × 3 × 0.3 × 0.3
Step-2: Group the factors into two groups so that
factors in both the groups are same
0.81 = (3 × 0.3) × (3 × 0.3)
= 0.9 × 0.9
Step-3: So,
[2]
0.25 = 0.5 × 0.5
[6]
0.81 = 0.9
0.64 = _____________________
0.5 0.25
0.5
0.25 = 0.5
[3]
0.04 = _____________________
0.64 = _______
[7]
0.04 = _______
[4]
0.01 = _____________________
0.49 = _______
[8]
0.01 = _______
[5]
0.16 = _____________________
0.16 = _______
Copyright  2009 by ExpertChild Inc.
0.49 = _____________________
1.44 = _____________________
1.44 = _______
[9]
0.09 = _____________________
0.09 = _______
6