What is a surd?
When the square root of a number is a decimal number (and not a whole number), it is called a surd.
Examples of surds are:
What is NOT a surd?
When a square root of a number is a whole number, it is not a surd.
Examples that are not surds are:
Find the square roots of these numbers - 1, 2, 3, 4, 5, 25, 50, 100.
Which are surds?
Answer
Surds are the square roots of 2, 3, 5, 50.
Simplify:
(a) 8
(b) 27
(c) 48
(d) 50
Answers:
Firstly, find the factors of the number where one of the factors is a square number such as 4, 9, 16, 25 and so on. Then simplify.
(a) 8 = 4 × 2 = 22
(b) 27 = 9 × 3 = 33
(c) 48 = 16 × 3 = 43
(d) 50 = 25 × 2 = 52
(a) 12
(b) 45
(c) 500
(d) 75
Answers
(a) 23
(b) 35
(c) 105
(d) 53
Make these entire surds:
(a) 32
(b) 25
(c) 35
(d) 57
Answers:
This is the reverse of Example One above.
(a) 32 = 9 × 2 = 18
(b) 25 = 4 × 5 = 20
(c) 35 = 9 × 5 = 45
(d) 57 = 25 × 7 = 175
(a) 53
(b) 210
(c) 37
(d) 73
Answers
(a) 75
(b) 40
(c) 63
(d) 147
Simplify these surds:
(a) 23 × 53
(b) 25 × 52
Answers:
(a) 23 × 53
= 4 × 3 × 25 × 3
= 900
= 30
(b) 25 × 52
= 4 × 5 × 25 × 2
= 1000
= 100 × 10
= 1010
Simplify these surds:
(a) | 85 |
25 |
(b) | 67 × 53 |
23 |
Answers:
(a) | 85 | = | 8 | = 4 |
25 | 2 |
(b) | 67 × 53 | = | 67 × 5 | = | 37 × 5 | = | 157 |
23 | 2 |
(a) 23 × 53
(b) | 43 |
26 |
Answers
(a) 30
(b) 2
Simplify these surds:
(a) | 3 |
2 |
(b) | 5 |
3 |
Answers:
If there is a surd on the bottom of a fraction, multiply both the top and the bottom of the fraction by that surd. Then simplify.
(a) | 3 | = | 32 | = | 32 |
2 | 2 × 2 | 2 |
(b) | 5 | = | 53 | = | 53 |
3 | 3 × 3 | 3 |
(a) | 7 |
2 |
(b) | 8 |
2 |
Answers
(a) | 7 2 |
2 |
(b) 42
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