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
√
9
)
(i)
(
−
1
11
)
(ii)
(
−
1
9
)
(iii)
(
−
1
7
)
(iv)
(
−
1
3
)
(v)
1
9
Question
2
2.
Rationalise the denominator of
1
(
√
2
−
√
6
)
(i)
(
−
1
4
√
2
−
3
2
)
(ii)
(
−
1
4
√
1
2
−
1
4
√
6
)
(iii)
(
−
1
4
√
2
−
1
4
√
6
)
(iv)
(
−
1
4
√
5
−
1
4
√
6
)
(v)
(
−
1
4
√
2
−
1
4
4
√
6
)
Question
3
3.
The rationalising factor of
(
−
8
√
54
)
=
(i)
√
8
(ii)
√
6
(iii)
√
3
(iv)
4
√
6
(v)
6
Question
4
4.
The rationalising factor of
(
3
√
4
+
6
√
6
)
=
(i)
(
6
−
6
4
√
6
)
(ii)
(
6
−
36
)
(iii)
(
6
−
6
√
6
)
(iv)
(
8
−
6
√
6
)
(v)
(
4
−
6
√
6
)
Question
5
5.
Rationalise the denominator of
1
(
2
√
5
+
6
√
7
)
(i)
(
−
1
116
√
5
+
3
116
√
7
)
(ii)
(
−
1
116
√
5
+
3
116
4
√
7
)
(iii)
(
−
1
116
√
2
+
3
116
√
7
)
(iv)
(
−
1
116
√
5
+
21
116
)
(v)
(
−
1
116
√
7
+
3
116
√
7
)
Question
6
6.
Rationalise the denominator of
(
−
2
−
√
2
)
(
−
√
2
−
√
7
)
=
(i)
(
−
2
5
√
2
−
2
5
+
2
5
√
7
+
1
5
√
14
)
(ii)
(
−
2
5
√
2
−
2
5
+
2
5
√
7
+
1
5
√
17
)
(iii)
(
−
2
5
√
2
−
2
7
+
2
5
√
7
+
1
5
√
14
)
(iv)
(
−
2
5
√
1
2
−
2
5
+
2
5
√
7
+
1
5
√
14
)
(v)
(
−
2
5
√
2
−
2
5
+
2
5
4
√
7
+
1
5
√
14
)
Question
7
7.
Rationalise the denominator of
(
−
3
√
5
−
√
2
)
(
−
5
√
9
+
3
√
8
)
=
(i)
(
5
17
√
5
+
5
51
4
√
2
+
2
17
√
10
+
4
51
)
(ii)
(
5
17
√
5
+
5
51
√
2
+
2
17
√
10
+
4
51
)
(iii)
(
5
17
√
3
+
5
51
√
2
+
2
17
√
10
+
4
51
)
(iv)
(
5
17
√
5
+
5
51
√
2
+
2
17
4
√
10
+
4
51
)
(v)
(
5
17
√
5
+
5
51
√
2
+
2
17
√
10
+
2
17
)
Question
8
8.
Rationalise the denominator of
1
(
−
√
3
)
(i)
(
−
1
3
√
6
)
(ii)
(
−
1
3
√
1
3
)
(iii)
(
−
1
3
4
√
3
)
(iv)
(
−
1
3
√
3
)
(v)
(
−
1
)
Question
9
9.
Rationalise the denominator of
1
(
2
+
√
2
)
(i)
(
1
−
1
2
√
2
)
(ii)
(
4
−
1
2
√
2
)
(iii)
(
1
−
1
2
4
√
2
)
(iv)
(
1
−
1
)
(v)
(
−
1
−
1
2
√
2
)
Question
10
10.
The rationalising factor of
4
√
76
=
(i)
4
√
19
(ii)
√
21
(iii)
√
19
(iv)
19
(v)
√
17
Question
11
11.
The rationalising factor of
(
−
2
√
2
−
9
√
5
)
=
(i)
(
−
2
√
-1
+
9
√
5
)
(ii)
(
−
2
√
2
+
9
√
5
)
(iii)
(
−
2
√
4
+
9
√
5
)
(iv)
(
−
2
√
2
+
9
4
√
5
)
(v)
(
−
2
√
2
+
45
)
Question
12
12.
Rationalise the denominator of
1
(
5
√
7
−
8
√
4
)
(i)
(
−
5
81
√
7
−
16
79
)
(ii)
(
−
5
81
√
7
−
16
83
)
(iii)
(
−
5
81
√
4
−
16
81
)
(iv)
(
−
5
81
√
9
−
16
81
)
(v)
(
−
5
81
√
7
−
16
81
)
Question
13
13.
Rationalise the denominator of
(
√
4
+
√
5
)
(
√
9
−
√
7
)
=
(i)
(
3
+
3
2
4
√
5
+
√
7
+
1
2
√
35
)
(ii)
(
3
+
3
2
√
5
+
4
√
7
+
1
2
√
35
)
(iii)
(
1
+
3
2
√
5
+
√
7
+
1
2
√
35
)
(iv)
(
3
+
3
2
√
5
+
√
7
+
1
2
√
37
)
(v)
(
3
+
3
2
√
5
+
√
7
+
1
2
√
35
)
Question
14
14.
Rationalise the denominator of
(
2
√
4
+
3
√
2
)
(
2
√
8
+
5
√
5
)
=
(i)
(
−
16
93
√
2
−
8
31
+
20
93
4
√
5
+
5
31
√
10
)
(ii)
(
−
16
93
√
1
2
−
8
31
+
20
93
√
5
+
5
31
√
10
)
(iii)
(
−
16
93
√
2
−
8
33
+
20
93
√
5
+
5
31
√
10
)
(iv)
(
−
16
93
√
2
−
8
31
+
20
93
√
5
+
5
31
√
12
)
(v)
(
−
16
93
√
2
−
8
31
+
20
93
√
5
+
5
31
√
10
)
Assignment Key
1) (ii)
2) (iii)
3) (ii)
4) (iii)
5) (i)
6) (i)
7) (ii)
8) (iv)
9) (i)
10) (iii)
11) (ii)
12) (v)
13) (v)
14) (v)
