igureMaths
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40 questions at your level
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Level 3
Level 4
Level 5
Simplifying surds
17 questions
Lesson
Not started
Mark as done
Write
48
\sqrt{48}
48
in the form
a
b
a\sqrt{b}
a
b
, where
a
a
a
and
b
b
b
are integers and
b
b
b
is as small as possible.
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Level 3
2 marks
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→
Mark as done
Simplify fully
5
12
−
2
27
5\sqrt{12} - 2\sqrt{27}
5
12
−
2
27
.
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Level 3
3 marks
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→
Mark as done
Work out
8
×
18
\sqrt{8} \times \sqrt{18}
8
×
18
. Give your answer as an integer.
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Level 3
2 marks
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→
Mark as done
Write
72
\sqrt{72}
72
in the form
a
b
a\sqrt{b}
a
b
, where
a
a
a
and
b
b
b
are integers and
b
b
b
is as small as possible.
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Level 3
2 marks
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→
Mark as done
Simplify fully
32
+
50
\sqrt{32} + \sqrt{50}
32
+
50
.
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Level 3
2 marks
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→
Mark as done
Work out
45
×
20
\sqrt{45} \times \sqrt{20}
45
×
20
. Give your answer as an integer.
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Level 3
2 marks
Start
→
Mark as done
(a)
Simplify fully
50
+
8
\sqrt{50} + \sqrt{8}
50
+
8
[2]
(b)
Expand and simplify
(
3
+
2
)
2
(3 + \sqrt{2})^2
(
3
+
2
)
2
[2]
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Level 3
4 marks
Start
→
Expanding brackets with surds
13 questions
Lesson
Not started
Mark as done
Expand and simplify
3
(
4
+
3
)
\sqrt{3}\,(4 + \sqrt{3})
3
(
4
+
3
)
.
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Level 3
2 marks
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→
Mark as done
Expand and simplify
5
(
5
−
2
)
\sqrt{5}\,(\sqrt{5} - 2)
5
(
5
−
2
)
.
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Level 3
2 marks
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→
Mark as done
Expand and simplify
(
3
+
2
)
(
3
−
2
)
(3 + \sqrt{2})(3 - \sqrt{2})
(
3
+
2
)
(
3
−
2
)
.
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Level 3
2 marks
Start
→
Mark as done
(a)
Rationalise the denominator of
12
3
\dfrac{12}{\sqrt{3}}
3
12
Give your answer in its simplest form. (2 marks)
(b)
Expand and simplify
(
5
+
2
)
(
5
−
2
)
(\sqrt{5} + 2)(\sqrt{5} - 2)
(
5
+
2
)
(
5
−
2
)
(2 marks)
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Level 3
4 marks
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→
Mark as done
(a)
Simplify fully
50
+
8
\sqrt{50} + \sqrt{8}
50
+
8
[2]
(b)
Expand and simplify
(
3
+
2
)
2
(3 + \sqrt{2})^2
(
3
+
2
)
2
[2]
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Level 3
4 marks
Start
→
Rationalising the denominator
16 questions
Lesson
Not started
Mark as done
Rationalise the denominator of
6
3
\dfrac{6}{\sqrt{3}}
3
6
. Give your answer in its simplest form.
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Level 3
2 marks
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→
Mark as done
Rationalise the denominator of
10
5
\dfrac{10}{\sqrt{5}}
5
10
. Give your answer in its simplest form.
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●●
Level 3
2 marks
Start
→
Mark as done
(a)
Rationalise the denominator of
12
3
\dfrac{12}{\sqrt{3}}
3
12
Give your answer in its simplest form. (2 marks)
(b)
Expand and simplify
(
5
+
2
)
(
5
−
2
)
(\sqrt{5} + 2)(\sqrt{5} - 2)
(
5
+
2
)
(
5
−
2
)
(2 marks)
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Level 3
4 marks
Start
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