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
5
√
5
(i)
1
25
√
5
(ii)
1
25
√
3
(iii)
1
25
4
√
5
(iv)
1
25
√
7
(v)
1
5
Question
2
2.
Rationalise the denominator of
1
(
−
√
9
+
√
3
)
(i)
(
1
2
−
1
6
√
3
)
(ii)
(
−
1
2
−
1
6
√
3
)
(iii)
(
−
1
2
−
1
6
4
√
3
)
(iv)
(
−
1
2
−
1
2
)
(v)
(
−
3
2
−
1
6
√
3
)
Question
3
3.
The rationalising factor of
√
74
=
(i)
√
77
(ii)
4
√
74
(iii)
√
74
(iv)
74
(v)
√
71
Question
4
4.
The rationalising factor of
(
−
4
√
6
+
2
√
7
)
=
(i)
(
−
4
√
4
−
2
√
7
)
(ii)
(
−
4
√
6
−
2
4
√
7
)
(iii)
(
−
4
√
6
−
14
)
(iv)
(
−
4
√
8
−
2
√
7
)
(v)
(
−
4
√
6
−
2
√
7
)
Question
5
5.
Rationalise the denominator of
1
(
21
−
9
√
3
)
(i)
(
7
66
+
3
22
)
(ii)
(
7
66
+
1
22
√
3
)
(iii)
(
3
22
+
1
22
√
3
)
(iv)
(
7
66
+
1
22
4
√
3
)
(v)
(
5
66
+
1
22
√
3
)
Question
6
6.
Rationalise the denominator of
(
√
5
−
√
6
)
(
−
√
8
+
√
3
)
=
(i)
(
−
2
5
√
10
+
2
5
4
√
12
−
1
5
√
15
+
1
5
√
18
)
(ii)
(
−
2
5
√
7
+
2
5
√
12
−
1
5
√
15
+
1
5
√
18
)
(iii)
(
−
2
5
√
10
+
2
5
√
12
−
1
5
4
√
15
+
1
5
√
18
)
(iv)
(
−
2
5
√
10
+
2
5
√
12
−
1
5
√
15
+
1
5
√
21
)
(v)
(
−
2
5
√
10
+
2
5
√
12
−
1
5
√
15
+
1
5
√
18
)
Question
7
7.
Rationalise the denominator of
(
3
√
2
−
2
√
3
)
(
−
4
√
3
−
4
√
9
)
=
(i)
(
1
8
√
6
−
1
4
−
3
8
√
2
+
1
4
√
5
)
(ii)
(
1
8
√
4
−
1
4
−
3
8
√
2
+
1
4
√
3
)
(iii)
(
1
8
√
6
−
1
4
−
3
8
4
√
2
+
1
4
√
3
)
(iv)
(
1
8
√
6
−
1
4
−
3
8
√
2
+
1
4
√
3
)
(v)
(
1
8
√
6
−
1
6
−
3
8
√
2
+
1
4
√
3
)
Question
8
8.
Rationalise the denominator of
1
8
√
9
(i)
1
22
(ii)
1
24
(iii)
(
−
1
24
)
(iv)
1
26
(v)
1
8
Question
9
9.
Rationalise the denominator of
1
(
√
9
−
√
8
)
(i)
(
1
+
2
√
2
)
(ii)
(
3
+
4
)
(iii)
(
3
+
2
4
√
2
)
(iv)
(
3
+
2
√
2
)
(v)
(
5
+
2
√
2
)
Question
10
10.
The rationalising factor of
5
√
67
=
(i)
√
67
(ii)
√
69
(iii)
4
√
67
(iv)
67
(v)
√
65
Question
11
11.
The rationalising factor of
(
−
9
√
3
−
9
√
7
)
=
(i)
(
−
9
√
3
+
9
√
7
)
(ii)
(
−
9
√
3
+
63
)
(iii)
(
−
9
√
1
3
+
9
√
7
)
(iv)
(
−
9
√
6
+
9
√
7
)
(v)
(
−
9
√
3
+
9
4
√
7
)
Question
12
12.
Rationalise the denominator of
1
(
√
5
+
9
√
7
)
(i)
(
−
1
562
√
5
+
9
562
√
7
)
(ii)
(
−
1
562
√
8
+
9
562
√
7
)
(iii)
(
−
1
562
√
2
+
9
562
√
7
)
(iv)
(
−
1
562
√
5
+
9
562
4
√
7
)
(v)
(
−
1
562
√
5
+
63
562
)
Question
13
13.
Rationalise the denominator of
(
−
√
7
−
√
3
)
(
√
9
+
√
8
)
=
(i)
(
−
3
√
5
−
3
√
3
+
2
√
14
+
2
√
6
)
(ii)
(
−
3
√
7
−
3
√
3
+
2
4
√
14
+
2
√
6
)
(iii)
(
−
3
√
7
−
3
4
√
3
+
2
√
14
+
2
√
6
)
(iv)
(
−
3
√
7
−
3
√
3
+
2
√
14
+
2
√
6
)
(v)
(
−
3
√
7
−
3
√
3
+
2
√
14
+
2
√
9
)
Question
14
14.
Rationalise the denominator of
(
3
√
3
+
3
√
8
)
(
√
6
−
4
√
9
)
=
(i)
(
−
27
46
√
2
−
24
23
)
(ii)
(
−
27
46
√
-1
−
8
23
√
3
)
(iii)
(
−
27
46
√
2
−
8
23
4
√
3
)
(iv)
(
−
27
46
√
4
−
8
23
√
3
)
(v)
(
−
27
46
√
2
−
8
23
√
3
)
Assignment Key
1) (i)
2) (ii)
3) (iii)
4) (v)
5) (ii)
6) (v)
7) (iv)
8) (ii)
9) (iv)
10) (i)
11) (i)
12) (i)
13) (iv)
14) (v)
