Exercise 1.5 Primes, Powers And Square Roots Worksheet - Heinemann Maths Zone Page 4
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1
2
3
4
5
6
7
8
9
10
11(e) 5 × 5 × 5 × 5 × 5 × 5
(f) 9 × 9 × 9 × 9 × 9
(g) 12 × 12 × 12 × 12 × 12
(h) 16 × 16 × 16 × 16 × 16 × 16 × 16 × 16 × 16
(i) 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6
(j) 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11
(k) seventeen cubed
(l) thirteen to the power of seven
(m) eight to the fourth power
(n) nine to the sixth
e
(o) eleven to the seventh
(p) nine to the third
eQuestions
8 Write each of these out in expanded form, then work out the answer.
e
3
4
6
5
(a) 2
(b) 2
(c) 2
(d) 2
Hint
8
7
6
7
(e) 1
(f) 0
(g) 0
(h) 1
3
5
4
4
(i) 10
(j) 10
(k) 6
(l) 8
3
4
6
6
(m) 11
(n) 12
(o) 4
(p) 6
9 What number do you have to cube to get each of these?
e
(a) 1
(b) 27
(c) 8
(d) 64
Hint
e
(e) 8000
(f) 1000
(g) 125
(h) 1 000 000
eQuestions
means cube root. The cube root of 27 is 3 because 3 × 3 × 3 = 27.
3
10
Evaluate, without using a calculator.
e
3
3
3
3
(a)
8
(b)
64
(c)
1000
(d)
1
Hint
3
3
3
3
(e)
0
(f)
125
(g)
8000
(h)
27 000
e
11 (a) Arrange these numbers in ascending order (smallest to largest).
Hint
5
4
200
3
6
5
4
, 5
, 1
, 10
, 4
, 5
(b) Arrange these numbers in descending order (largest to smallest).
2
5
1000
100
2
3
100
, 10
, 1
, 0
, 3
, 2
12 (a) Copy and complete:
= 10
1
10
= 10 × 10 = 100
2
10
= 10 × 10 × 10 = 1000
3
10
=
4
10
=
5
10
100
(b) The number 10
was called a googol by the mathematician
Edward Kasner.
(i) How many times is 10 multiplied by itself to get a googol?
(ii) Look at the pattern in part (a). If you were to work out what a
googol is equal to, how many zeros would follow the 1?
e
(c) If you raise the number 10 to the power of a googol, you get a
.au
number called a googolplex.
(i) How many times is 10 multiplied by itself to get a googolplex?
(ii) If you were to work out what a googolplex is equal to, how many
zeros would follow the 1? How much time do you think you save
by writing a googolplex in index form?
20
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