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Surds Questions and Answers
Simplify #(sqrt 54 + 3 sqrt 3)/(sqrt 3)#
KCSE 2018 Paper 2 Question 5
(2m 31s)
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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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