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Surds Questions and Answers
Simplify
√
3
√
3
-
√
2
.
KCSE 2009 Paper 2 Question 10
(2m 46s)
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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-sqrt 7)
3.
Simplify
(4)/(sqrt 5 + sqrt 2)-(3)/(sqrt5-sqrt2)
4.
Simplify
(sqrt 11)/(sqrt 11-sqrt 7)
5.
Simplify
(sqrt 54 + 3 sqrt 3)/(sqrt 3)
6.
Simplify the expression below, leaving the answer in the form
a sqrt b + c
where a, b and c are integers.
(sqrt 48)/(sqrt 5 + sqrt 3)
7.
Simplify the expression below, leaving the answer in the form
a sqrt b +c
where a, b and c are integers.
(sqrt 5)/(sqrt 5 - 2)
8.
Simplify the following expression giving your answer in the form
a +b\sqrt c
where a, b and c are integers.
(sqrt 5 + 3)/(sqrt 5 - 2)
9.
Write sin
45^o
in the form
(1)/(sqrt a)
where a is a positive integer. Hence simplify
(sqrt 8)/(1+sin 45^o)
, leaving the answer in surd form.
10.
Simplify
(4)/(sqrt 5 + sqrt 2) - (3)/(sqrt 5 - sqrt 2
11.
Simplify
(sqrt 3)/(sqrt 3 - sqrt 2)
12.
Without using a calculator or mathematical tables, express
(sqrt 3)/(1 - cos 30^o)
in surd form and simplify.
13.
Simplify
(3)/(sqrt 5 - 2) - (1)/(sqrt 5)
leaving the answer in the form
a +b sqrt c
where a, b and c are rational numbers.
14.
Simplify
(1+ sqrt 3)(1 - sqrt 3)
. Hence evaluate
(1)/(1 + sqrt 3)
to 3 significant figures given that
sqrt 3=1.7321
15.
Without using a calculator or mathematical tables, simplify
(3 sqrt 2 - sqrt 3)/(2 sqrt 3 - sqrt 2)
16.
Without using mathematical tables, simplify
(sqrt 63 + sqrt 72)/(sqrt 32 + sqrt 28)
17.
Without using mathematical tables, simplify
(2)/(3 - sqrt 7) - frac(2)(3 + sqrt 7)
in the form
a sqrt b
18.
Given that
a=(1)/(sqrt 3)
and b =
sqrt 13
, express
2 sqrt 3 - 6 sqrt 39
in terms of a and b and simplify.
19.
Simplify as far as possible, leaving your answer the form of a surd.
(1)/(sqrt 14 - 2 sqrt 3) - (1)/(sqrt 14 + 2 sqrt 3)
20.
If
(sqrt 14)/(sqrt 7 - sqrt 2) - (sqrt 14)/(sqrt 7 + sqrt 2) = a sqrt 7 + b sqrt 2
, find the values of a and b where a and b are rational numbers.
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