Download Squares and square roots

NUMBER AND ALGEBRA • NUMBER AND PLACE VALUE
REMEMBER
1. Square numbers are written using an index (or power) of 2 and are found by
multiplying the number by itself.
2. The opposite of squaring a number is finding the square root of a number.
3. To find the square root of a number we can use our knowledge of square numbers
or use a calculator.
EXERCISE
3C
INDIVIDUAL
PATHWAYS
eBoo
k plus
eBook
Activity 3-C-1
Squares and square
roots
doc-1681
Activity 3-C-2
More squares and
square roots
doc-1682
Activity 3-C-3
Advanced squares
and square roots
doc-1683
Squares and square roots
FLUENCY
1 Evaluate and verify your answers with a calculator.
a 82
b 112
c 152
d 252
2 WE10 a Find the square numbers between 50 and 100.
b Find the square numbers between 160 and 200.
3 WE11 Write two whole square numbers between which each of the following will lie.
a 6.42
b 7.82
c 9.22
d 12.52
4 WE12a Find:
a
25
81
b
c
144
d
400
d
160 000
5 WE12b Find and verify your answers with a calculator.
a
4900
b
14 400
c
360 000
6 WE13 Between which two numbers will 60 lie?
7 Write the two whole numbers between which each of the following will lie.
a
14
b
90
c
200
2
d
UNDERSTANDING
8 a Find the even square numbers between 10 and 70.
b Find the odd square numbers between 50 and 120.
9 MC For which of the following square roots can we calculate an exact answer?
A
10
B
25
C
50
D
75
E
82
10 MC For which of the following square roots can we NOT calculate the exact value?
A
160
B
400
C
900
D
11 Evaluate the following. Verify your answers with a calculator.
a 22 +
25
b 92 - 36
c 52 ì 22 ì
49
d 32 + 22 ì 16
e 32 - 22 ó
f
80
4 + 49
9 ì 42 - 144 ó 22
Maths Quest 7 for the Australian Curriculum
2500
E
3600
NUMBER AND ALGEBRA • NUMBER AND PLACE VALUE
REASONING
12 Explain why we cannot find the exact value of 10 .
13 Megan has 3 game scores that happen to be square numbers. The first 2 scores have the same
three digits. The total of the 3 scores is 590. What are the 3 scores?
14 The difference of the squares of two consecutive odd numbers is 32. What are the two odd
numbers?
REFLECTION
Because square numbers form a
shape (or figure), they are called
figurate numbers. Can you think of
any other figurate numbers?
3D
Cubes and cube roots
Cubic numbers
■
Cubic numbers are numbers that can be arranged in a cube, as shown below.
13 = 1
23 = 8
33 = 27
Chapter 3
Indices and primes
81