Exercise 1.5 Primes, Powers And Square Roots Worksheet - Heinemann Maths Zone Page 3
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11exercise 1.5
Primes, powers and
square roots
Preparation: Exercise 1.4
1 Complete these factor trees, then write each number as a product of its
prime factors.
16
50
(a)
(b)
e
Worksheet C1.8
8
2
16 =
×
×
×
50 =
×
×
(c)
100
(d)
96
10
3
100 =
×
×
×
96 =
×
×
×
×
×
e
Interactive
2 Express each number as a product of its prime factors.
e
(a) 8
(b) 12
(c) 18
(d) 26
Hint
(e) 20
(f) 48
(g) 68
(h) 44
e
eQuestions
(i) 64
(j) 72
(k) 108
(l) 144
e
eQuestions
(m) 140
(n) 1000
(o) 800
(p) 400
e
Worksheet C1.9
3
3
Find three different numbers that can each be expressed as a product of
four prime factors. (The product may contain repeated factors.)
4 Simplify these with your calculator, using the shortest method possible.
e
2
2
2
2
(a) 21
(b) 18
(c) 48
(d) 61
Hint
2
2
2
2
(e) 75
(f) 88
(g) 540
(h) 439
− 203
− 1341
2
2
2
2
(i) 2305
(j) 1766
(k) 43
(l) 74
× 14
× 22
+ 41
− 14
2
2
2
2
2
2
2
2
(m) 68
(n) 37
(o) 26
(p) 23
5 What number do you have to square to get each of these?
e
(a) 9
(b) 4
(c) 49
(d) 64
Hint
e
(e) 81
(f) 25
(g) 144
(h) 10 000
eQuestions
6 Evaluate the following.
(a)
25
(b)
49
What number times
itself gives 25?
(c)
36
(d)
64
100
121
(e)
(f)
(g)
196
(h)
169
(i)
1
(j)
0
(k)
4900
(l)
400
(m)
1600
(n)
2500
e
(o)
360 000
(p)
1 000 000
eQuestions
7 Write each of these in index form. (Don’t work out the answer.)
e
(a) 8 × 8 × 8
(b) 4 × 4 × 4 × 4 × 4 × 4
Hint
(c) 9 × 9 × 9 × 9
(d) 7 × 7 × 7
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