EduSahara™ Assignment
Name : Rationalising the Denominator
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Rationalise the denominator of
1
3
√
7
(i)
1
21
√
9
(ii)
1
21
√
5
(iii)
1
3
(iv)
1
21
4
√
7
(v)
1
21
√
7
Question
2
2.
Rationalise the denominator of
1
(
√
6
+
√
3
)
(i)
(
1
3
√
6
−
1
)
(ii)
(
1
3
√
6
−
1
3
√
3
)
(iii)
(
1
3
√
6
−
1
3
4
√
3
)
(iv)
(
1
3
√
3
−
1
3
√
3
)
(v)
(
1
3
√
8
−
1
3
√
3
)
Question
3
3.
The rationalising factor of
(
−
5
√
74
)
=
(i)
√
74
(ii)
4
√
74
(iii)
√
76
(iv)
74
(v)
√
72
Question
4
4.
The rationalising factor of
(
−
4
√
3
+
5
√
8
)
=
(i)
(
−
4
√
3
−
10
√
2
)
(ii)
(
−
4
√
3
−
20
)
(iii)
(
−
4
√
3
−
10
4
√
2
)
(iv)
(
−
4
√
6
−
10
√
2
)
(v)
(
−
4
−
10
√
2
)
Question
5
5.
Rationalise the denominator of
1
(
3
√
9
+
2
√
7
)
(i)
(
9
53
−
2
53
√
7
)
(ii)
(
11
53
−
2
53
√
7
)
(iii)
(
7
53
−
2
53
√
7
)
(iv)
(
9
53
−
14
53
)
(v)
(
9
53
−
2
53
4
√
7
)
Question
6
6.
Rationalise the denominator of
(
−
√
6
+
√
7
)
(
−
√
7
−
√
5
)
=
(i)
(
1
2
√
42
−
7
2
−
1
2
√
30
+
1
2
√
35
)
(ii)
(
1
2
√
42
−
13
4
−
1
2
√
30
+
1
2
√
35
)
(iii)
(
1
2
√
39
−
7
2
−
1
2
√
30
+
1
2
√
35
)
(iv)
(
1
2
√
42
−
7
2
−
1
2
4
√
30
+
1
2
√
35
)
(v)
(
1
2
√
42
−
7
2
−
1
2
√
30
+
1
2
√
37
)
Question
7
7.
Rationalise the denominator of
(
√
4
−
4
√
3
)
(
−
2
√
7
−
3
√
2
)
=
(i)
(
−
2
5
√
7
+
4
5
√
21
+
3
5
√
2
−
6
5
√
6
)
(ii)
(
−
2
5
√
7
+
4
5
√
21
+
3
5
√
2
−
6
5
√
9
)
(iii)
(
−
2
5
√
5
+
4
5
√
21
+
3
5
√
2
−
6
5
√
6
)
(iv)
(
−
2
5
√
7
+
4
5
4
√
21
+
3
5
√
2
−
6
5
√
6
)
(v)
(
−
2
5
√
7
+
4
5
√
21
+
3
5
4
√
2
−
6
5
√
6
)
Question
8
8.
Rationalise the denominator of
1
4
√
7
(i)
1
28
4
√
7
(ii)
1
28
√
4
(iii)
1
28
√
9
(iv)
1
4
(v)
1
28
√
7
Question
9
9.
Rationalise the denominator of
1
(
√
6
−
√
9
)
(i)
(
−
1
3
√
6
+
0
)
(ii)
(
−
1
3
√
6
−
2
)
(iii)
(
−
1
3
√
8
−
1
)
(iv)
(
−
1
3
√
3
−
1
)
(v)
(
−
1
3
√
6
−
1
)
Question
10
10.
The rationalising factor of
(
−
8
√
41
)
=
(i)
41
(ii)
√
41
(iii)
4
√
41
(iv)
√
43
(v)
√
39
Question
11
11.
The rationalising factor of
(
6
+
4
√
8
)
=
(i)
(
3
−
8
√
2
)
(ii)
(
6
−
8
4
√
2
)
(iii)
(
6
−
16
)
(iv)
(
9
−
8
√
2
)
(v)
(
6
−
8
√
2
)
Question
12
12.
Rationalise the denominator of
1
(
−
6
√
9
−
8
√
6
)
(i)
(
1
2
−
2
15
√
6
)
(ii)
(
1
10
−
2
15
√
6
)
(iii)
(
3
10
−
2
15
4
√
6
)
(iv)
(
3
10
−
4
5
)
(v)
(
3
10
−
2
15
√
6
)
Question
13
13.
Rationalise the denominator of
(
−
√
8
−
√
7
)
(
−
3
+
√
5
)
=
(i)
(
3
2
√
2
+
3
4
√
7
+
1
2
√
10
+
1
4
√
35
)
(ii)
(
3
2
√
2
+
3
4
√
7
+
1
2
4
√
10
+
1
4
√
35
)
(iii)
(
3
2
√
2
+
3
4
4
√
7
+
1
2
√
10
+
1
4
√
35
)
(iv)
(
3
2
√
2
+
3
4
√
7
+
1
2
√
10
+
1
4
√
37
)
(v)
(
3
2
√
1
2
+
3
4
√
7
+
1
2
√
10
+
1
4
√
35
)
Question
14
14.
Rationalise the denominator of
(
−
2
√
5
−
3
√
2
)
(
−
3
√
4
+
5
√
5
)
=
(i)
(
−
12
89
√
2
−
18
89
√
2
−
50
89
−
15
89
√
10
)
(ii)
(
−
12
89
√
5
−
18
89
√
2
−
50
89
−
15
89
√
13
)
(iii)
(
−
12
89
√
5
−
18
89
4
√
2
−
50
89
−
15
89
√
10
)
(iv)
(
−
12
89
√
5
−
18
89
√
2
−
50
91
−
15
89
√
10
)
(v)
(
−
12
89
√
5
−
18
89
√
2
−
50
89
−
15
89
√
10
)
Assignment Key
1) (v)
2) (ii)
3) (i)
4) (i)
5) (i)
6) (i)
7) (i)
8) (v)
9) (v)
10) (ii)
11) (v)
12) (v)
13) (i)
14) (v)
