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Surds Questions and Answers
Without using mathematical tables, simplify
√
63
+
√
72
√
32
+
√
28
.
KCSE 2005 Paper 2 Question 2
(6m 18s)
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1.
Without using mathematical tables or a calculator, evaluate
sin
30
o
-
sin
60
o
tan
60
o
2.
Simplify
3
3
-
√
7
3.
Simplify
4
√
5
+
√
2
-
3
√
5
-
√
2
4.
Simplify
√
11
√
11
-
√
7
5.
Simplify
√
54
+
3
√
3
√
3
6.
Simplify the expression below, leaving the answer in the form
a
√
b
+
c
where a, b and c are integers.
√
48
√
5
+
√
3
7.
Simplify the expression below, leaving the answer in the form
a
√
b
+
c
where a, b and c are integers.
√
5
√
5
-
2
8.
Simplify the following expression giving your answer in the form
a
+
b
√
c
where a, b and c are integers.
√
5
+
3
√
5
-
2
9.
Write sin
45
o
in the form
1
√
a
where a is a positive integer. Hence simplify
√
8
1
+
sin
45
o
, leaving the answer in surd form.
10.
Simplify
4
√
5
+
√
2
-
3
√
5
-
√
2
11.
Simplify
√
3
√
3
-
√
2
12.
Without using a calculator or mathematical tables, express
√
3
1
-
cos
30
o
in surd form and simplify.
13.
Simplify
3
√
5
-
2
-
1
√
5
leaving the answer in the form
a
+
b
√
c
where a, b and c are rational numbers.
14.
Simplify
(
1
+
√
3
)
(
1
-
√
3
)
. Hence evaluate
1
1
+
√
3
to 3 significant figures given that
√
3
=
1.7321
15.
Without using a calculator or mathematical tables, simplify
3
√
2
-
√
3
2
√
3
-
√
2
16.
Without using mathematical tables, simplify
√
63
+
√
72
√
32
+
√
28
17.
Without using mathematical tables, simplify
2
3
-
√
7
-
2
3
+
√
7
in the form
a
√
b
18.
Given that
a
=
1
√
3
and b =
√
13
, express
2
√
3
-
6
√
39
in terms of a and b and simplify.
19.
Simplify as far as possible, leaving your answer the form of a surd.
1
√
14
-
2
√
3
-
1
√
14
+
2
√
3
20.
If
√
14
√
7
-
√
2
-
√
14
√
7
+
√
2
=
a
√
7
+
b
√
2
, find the values of a and b where a and b are rational numbers.
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