igureMaths
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40 questions at your level
Difficulty
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Level 3
Level 4
Level 5
Simplifying surds
17 questions
Lesson
Not started
Mark as done
Simplify fully
200
+
18
−
50
\sqrt{200} + \sqrt{18} - \sqrt{50}
200
+
18
−
50
.
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Level 4
3 marks
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→
Mark as done
Simplify fully
3
8
−
18
+
2
3\sqrt{8} - \sqrt{18} + \sqrt{2}
3
8
−
18
+
2
.
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Level 4
3 marks
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→
Mark as done
(a)
Write
180
\sqrt{180}
180
in the form
a
5
a\sqrt{5}
a
5
, where
a
a
a
is an integer.
(b)
Hence, or otherwise, work out
180
5
\dfrac{\sqrt{180}}{\sqrt{5}}
5
180
.
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Level 4
3 marks
Start
→
Mark as done
(a)
Rationalise the denominator of
1
11
\dfrac{1}{\sqrt{11}}
11
1
(1 mark)
(b)
Simplify fully
63
−
28
\sqrt{63} - \sqrt{28}
63
−
28
(2 marks)
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Level 4
3 marks
Start
→
Expanding brackets with surds
13 questions
Lesson
Not started
Mark as done
Expand and simplify
(
2
+
5
)
(
3
−
5
)
(2 + \sqrt{5})(3 - \sqrt{5})
(
2
+
5
)
(
3
−
5
)
.
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Level 4
3 marks
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→
Mark as done
Write
(
4
−
2
)
2
(4 - \sqrt{2})^2
(
4
−
2
)
2
in the form
a
+
b
2
a + b\sqrt{2}
a
+
b
2
, where
a
a
a
and
b
b
b
are integers.
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Level 4
2 marks
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→
Mark as done
Show that
(
5
+
3
)
(
5
−
3
)
=
22
(5 + \sqrt{3})(5 - \sqrt{3}) = 22
(
5
+
3
)
(
5
−
3
)
=
22
.
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Level 4
2 marks
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→
Mark as done
Write
(
7
+
1
)
2
(\sqrt{7} + 1)^2
(
7
+
1
)
2
in the form
a
+
b
7
a + b\sqrt{7}
a
+
b
7
, where
a
a
a
and
b
b
b
are integers.
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Level 4
2 marks
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→
Mark as done
Expand and simplify
(
2
3
+
1
)
(
3
−
4
)
(2\sqrt{3} + 1)(\sqrt{3} - 4)
(
2
3
+
1
)
(
3
−
4
)
.
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Level 4
3 marks
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→
Mark as done
A square has sides of length
(
2
+
5
)
(2 + \sqrt{5})
(
2
+
5
)
cm.
Work out the area of the square. Give your answer in the form
a
+
b
5
a + b\sqrt{5}
a
+
b
5
, where
a
a
a
and
b
b
b
are integers.
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Level 4
2 marks
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→
Rationalising the denominator
16 questions
Lesson
Not started
Mark as done
Rationalise the denominator of
5
+
2
2
\dfrac{5 + \sqrt{2}}{\sqrt{2}}
2
5
+
2
. Simplify your answer.
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Level 4
2 marks
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→
Mark as done
Rationalise the denominator of
4
3
+
5
\dfrac{4}{3 + \sqrt{5}}
3
+
5
4
. Give your answer in its simplest form.
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Level 4
3 marks
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→
Mark as done
Rationalise the denominator of
3
+
6
3
\dfrac{3 + \sqrt{6}}{\sqrt{3}}
3
3
+
6
. Simplify your answer.
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Level 4
3 marks
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→
Mark as done
Rationalise the denominator of
6
7
−
1
\dfrac{6}{\sqrt{7} - 1}
7
−
1
6
. Give your answer in its simplest form.
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Level 4
3 marks
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→
Mark as done
Rationalise the denominator of
14
3
−
2
\dfrac{14}{3 - \sqrt{2}}
3
−
2
14
Give your answer in the form
a
+
b
2
a + b\sqrt{2}
a
+
b
2
, where
a
a
a
and
b
b
b
are integers. (3 marks)
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Level 4
3 marks
Start
→
Mark as done
(a)
Rationalise the denominator of
1
11
\dfrac{1}{\sqrt{11}}
11
1
(1 mark)
(b)
Simplify fully
63
−
28
\sqrt{63} - \sqrt{28}
63
−
28
(2 marks)
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Level 4
3 marks
Start
→