1. Indices and Surds
iGCSE (2021 Edition)
1.07 Adding and subtracting surds
Worksheet
1
State whether the following equations are true or false:
a
\sqrt{11}+\sqrt{5}=\sqrt{16}
b
\sqrt{4}+\sqrt{4} = 4
c
5-\sqrt{5}=\sqrt{5}
d
\sqrt{1}+\sqrt{4}=\sqrt{25}
e
\sqrt{16}+\sqrt{9}=7
f
\sqrt{32}+\sqrt{2}=5\sqrt{2}
g
\sqrt{25}-\sqrt{9}=\sqrt{16}
h
\sqrt{100}-\sqrt{64}=2
2
Does the following expression hold for any choice of k or m?
\sqrt{k}+\sqrt{m} = \sqrt{k+m}
3
Simplify the following:
a
10 \sqrt{2}+14 \sqrt{2}
b
\sqrt{6}+14 \sqrt{6}
c
\sqrt{10}-20 \sqrt{10}
d
12 \sqrt{2}-3 \sqrt{2}
e
4 \sqrt{3}-12 \sqrt{3}
f
18 \sqrt{5}-15 \sqrt{5}
g
6 \sqrt{7}-8 \sqrt{7}
h
6 \sqrt{2}+13\sqrt{2}
4
Simplify the following:
a
5\sqrt{5}+9\sqrt{5}-7\sqrt{5}
b
10\sqrt{6}-3\sqrt{6}+20\sqrt{6}
c
7\sqrt{6}+18\sqrt{6}-9\sqrt{6}
d
19 \sqrt{6} - 4 \sqrt{6} - 2 \sqrt{6}
e
8 \sqrt{5}- 9 \sqrt{5} - 14 \sqrt{5}
f
18 \sqrt{10}- 9 \sqrt{10} - 7 \sqrt{10}
5
Simplify the following:
a
8 \sqrt{2} + 2 \sqrt{11} + 2 \sqrt{2} + 4 \sqrt{11}
b
10 \sqrt{2} + 5 \sqrt{3} + 4 \sqrt{2} - 7 \sqrt{3}
c
6 \sqrt{7} + 7 \sqrt{5} - 3 \sqrt{7} + 8 \sqrt{5}
d
18 \sqrt{7} - 9 \sqrt{3} + 20 \sqrt{7} + 11 \sqrt{3}
e
20 \sqrt{7} + 7 \sqrt{11} + \sqrt{7} + 25 \sqrt{11}
f
7 \sqrt{11} + 28 \sqrt{5} - 25 \sqrt{11} - 11 \sqrt{5}
g
20 \sqrt{11} + 26 \sqrt{5} + 22 \sqrt{5} - 15 \sqrt{11}
6
Simplify the following:
a
\sqrt{3} + \sqrt{48}
b
\sqrt{180} + \sqrt{5}
c
\sqrt{45} + \sqrt{80}
d
\sqrt{245} - \sqrt{5}
e
\sqrt{48} - \sqrt{12}
f
3 \sqrt{27} + 2 \sqrt{12}
g
3 \sqrt{192} -2 \sqrt{108}
h
\frac{3 \sqrt{2}}{2} + \frac{\sqrt{2}}{6}.
7
Find the perimeter of the triangle in simplified surd form.
8
An athlete is participating in a race around the track shown in the diagram, which has dimensions in kilometres.
What is the length of one lap around this race track?
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