Exercise 1.4
Powers and roots
1 Find the value of each of these. b 33 a 23
c 43
d 53
2 Find the value of each of these. b 34 a 24
c 44
d 104
e 10³
3 a 44 is equal to 2N. What number is N ? b 93 is equal to 3M. What number is M ? 4 The number 100 has two square roots. a What is their sum? b What is their product? 5 Find the square roots of each number. a 1 b 36 c 169
d 256
e 361
3 6 a Show that 3 −1 = 32 + 3 + 1. 2 3 4 b Show that −1 = 42 + 4 + 1. 3 c Write a similar expression involving 53.
7 The numbers in the box are all identical in value. Use this fact to write down: b 3 4096 . a 4096 8 Find the value of: b a 121 9 Find the value of: b a 38
3
289
c
125
c
3
212
400
d
27
d
10 113 = 1331. Use this fact to work out: b 3 1331 . a 114 11 Explain why Alicia is correct. A square root of 25 could be less than a square root of 16.
10
1 Integers, powers and roots
1. 3
1000
46
163
642
4096