Name:
Exam Style Questions
Surds
Equipment needed: Pen
Guidance
1. Read each question carefully before you begin answering it.
2. Check your answers seem right.
3. Always show your workings
Video Tutorial
www.corbettmaths.com/contents
Videos 305, 306, 307, 308
Answers and Video Solutions
© Corbettmaths 2025
1.
Evaluate the following
(a)
3×
7
.........................
(1)
(b)
24 ÷
6
.........................
(2)
(c)
2 3×3 5
.........................
(2)
(d)
10 8 ÷ 2 2
.........................
(2)
2.
Simplify (
3)
2
.........................
(1)
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3.
Work out the exact value of (
2)
4
.........................
(1)
4.
(a) Express
75 in its simplest form.
.........................
(1)
(b) Express
32 in its simplest form.
.........................
(1)
(c) Express
8 in its simplest form.
.........................
(1)
(d) Express
200 in its simplest form.
.........................
(1)
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5.
Simplify
5×
10
.........................
(2)
6.
Simplify fully
(a)
50 +
32
.........................
(2)
(b)
80 +
20
.........................
(2)
(c)
200 −
72
.........................
(2)
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(d) 3
12 +
75
.........................
(3)
7.
Tilly has been asked to work out
Tilly says the answer is
2+
8
10 as 2 + 8 = 10
Is Tilly correct?
Explain your answer.
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
(2)
8.
Express
2+
98 in the form a 2 where a is an integer.
.........................
(2)
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9.
Write
150 +
24 in the form k 6
.........................
(2)
10.
Shown below is a rectangle.
5 2 cm
2 cm
(a) Find the perimeter of the rectangle.
.........................cm
(2)
(b) Find the area of the rectangle.
.........................cm²
(2)
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11.
Write each of these in the form a
(a)
6×
3 , where a is an integer.
8
.........................
(2)
(b)
27 +
75
.........................
(2)
12.
Rationalise the denominator of
15
5
.........................
(2)
13.
Simplify fully
600 +
24
.........................
(2)
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14.
(a) Rationalise the denominator of
12
3
.........................
(2)
(b) Evaluate
2×
32
.........................
(2)
(c) Expand and simplify (
3+
5)
2
.........................
(2)
(d) Evaluate (5 +
2 )(5 −
2)
.........................
(2)
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15.
(a) Simplify fully
3 ( 27 −
3)
.........................
(2)
(b) Given that a =
2 b=
work out the value of
15 c =
30
b
ac
write your answer in its simplest form
.........................
(3)
16.
Rationalise the denominator of
12
7 3
.........................
(2)
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17.
Given that a =
(a)
3 and b =
48
nd the value of a 2
.........................
(1)
(b) show that (a + b)2 = 75
.........................
(3)
18.
Expand and simplify (3 +
8 )(4 +
Give your answer in the form a + b
2)
2 where a and b are integers.
.........................
(4)
fi
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19.
Simplify 5
8+
18
.........................
(2)
20.
Rationalise the denominator of
8
2
.........................
(2)
21.
Expand and simplify (
7−
3)
2
.........................
(2)
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22.
Write
11 +
99 in the form a b where a and b are integers.
.........................
(2)
23.
Expand (8 −
3 ) giving your answer in form a + b 3
2
.........................
(2)
24.
Show that (
2 + 3 8 ) = 98
2
.........................
(3)
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25.
The midpoints of the sides of a square of side 10cm are joined to form another
square.
This process is then repeated to create the shaded square.
Find the area of the shaded square.
.........................cm²
(4)
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26.
Simplify
80 −
10
5
.........................
(3)
27.
Given that
10 −
32
2
=a+b 2
where a and b are integer.
Find the values of a and b.
a = .........................
b = .........................
(4)
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28.
A shed has dimensions, in metres, of
Height =
5
Width =
6
Find the volume of the shed.
Give your answer in the form a
Length =
9
2
15 , where a is an integer.
.........................m³
(3)
29.
(a) Simplify
2y+
(b) Simplify fully
2y+
2y×
2y
2y×
2y
.........................
(1)
.........................
(2)
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30.
c=
9
2 y
d=
4
y
Work out cd
.........................
(3)
31.
y=
4 10
5
Work out the value of y 3
.........................
(3)
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32.
(3 + c 5 ) = d + 24 5
2
Work out the values of c and d.
c = .........................
d = .........................
(4)
33.
300 − 2 x = 4 3
Work out the value of x
.........................
(3)
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34.
Given that
1
2
+
25
12 =
a 3
b
Work out the values of a and b
.........................
(3)
35.
Write
4
5
−
2
2
in the form a 5
9
.........................
(4)
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36.
Write
6
1
2
+
2
in the form a
2
.........................
(4)
37.
Show that
16
11 − 3
can be written in the form a + b
11
.........................
(4)
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38.
Show that
6
2−
3
can be written in the form a + b
3
.........................
(4)
39.
Write
4 2
3+
2
+
6
2
in the form
a 2−b
c
.........................
(4)
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40.
Write
2−2
3 2+4
in the form a + b
2 , where a and b are integers.
.........................
(4)
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