EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Find the rational number at the point labelled with letter P
(i)
(
-51
10
)
(ii)
(
-49
8
)
(iii)
(
-17
2
)
(iv)
(
-53
8
)
(v)
(
-51
8
)
Question
2
2.
Find the position of the rational number
(
-41
9
)
on the number line
(i)
O
(ii)
D
(iii)
G
(iv)
Q
(v)
K
Question
3
3.
Rationalise the denominator of
1
(
−
√
4
−
√
3
)
(i)
(
−
4
+
√
3
)
(ii)
(
−
2
+
√
3
)
(iii)
(
−
2
+
3
)
(iv)
(
−
2
+
4
√
3
)
(v)
(
0
+
√
3
)
Question
4
4.
Which of the following is an irrational number?
(i)
9
12
(ii)
5.8889
(iii)
(-8)
(iv)
25
(v)
√
12
Question
5
5.
Which of the following are true?
a)
5
19
✕
24
11
=
24
11
✕
5
19
b)
7
5
÷
24
11
=
24
11
÷
7
5
c)
7
5
−
69
17
=
69
17
−
7
5
d)
5
19
+
69
17
=
69
17
+
5
19
(i)
{b,c,a}
(ii)
{a,d}
(iii)
{b,d,a}
(iv)
{c,d}
(v)
{b,a}
Question
6
6.
Find the position of the rational number
19
6
on the number line
(i)
M
(ii)
G
(iii)
Q
(iv)
N
(v)
D
Question
7
7.
Which of the following is a rational number?
(i)
3
√
95
(ii)
√
43
(iii)
3
√
41
(iv)
2
8
(v)
3
√
38
Question
8
8.
Rationalise the denominator of
1
(
−
6
√
9
+
5
√
7
)
(i)
(
−
18
149
−
35
149
)
(ii)
(
−
20
149
−
5
149
√
7
)
(iii)
(
−
18
149
−
5
149
√
7
)
(iv)
(
−
18
149
−
5
149
4
√
7
)
(v)
(
−
16
149
−
5
149
√
7
)
Question
9
9.
Which of the following are true?
a)
rational numbers are closed under multiplication
b)
rational numbers are closed under addition
c)
rational numbers are closed under subtraction
d)
rational numbers are closed under division
(i)
{d,c}
(ii)
{a,b,c}
(iii)
{d,a}
(iv)
{d,b}
(v)
{d,a,b}
Question
10
10.
Find the difference of the rational numbers at the points labelled with letters P and Q
(i)
(
-2
5
)
(ii)
(
-2
3
)
(iii)
0
(iv)
(
-4
5
)
(v)
(
-2
7
)
Question
11
11.
Find the product of the rational numbers at the points labelled with letters R and S
(i)
3361
100
(ii)
673
20
(iii)
471
14
(iv)
1143
34
(v)
3363
100
Question
12
12.
The rationalising factor of
(
−
8
√
2
+
√
7
)
=
(i)
(
−
8
√
2
−
√
7
)
(ii)
(
−
8
√
-1
−
√
7
)
(iii)
(
−
8
√
4
−
√
7
)
(iv)
(
−
8
√
2
−
7
)
(v)
(
−
8
√
2
−
4
√
7
)
Question
13
13.
Find the difference of the rational numbers at the points labelled with letters G and H
(i)
(
-2
5
)
(ii)
(
-2
7
)
(iii)
0
(iv)
(
-2
3
)
(v)
(
-4
5
)
Question
14
14.
Rationalise the denominator of
1
9
√
2
(i)
1
18
√
-1
(ii)
1
9
(iii)
1
18
√
2
(iv)
1
18
4
√
2
(v)
1
18
√
4
Question
15
15.
Find the product of the rational numbers at the points labelled with letters Q and R
(i)
1411
20
(ii)
141
2
(iii)
1271
18
(iv)
1413
20
(v)
1409
20
Question
16
16.
The rationalising factor of
√
51
=
(i)
51
(ii)
4
√
51
(iii)
√
54
(iv)
√
48
(v)
√
51
Question
17
17.
Find the rational number at the point labelled with letter R
(i)
23
3
(ii)
23
(iii)
25
3
(iv)
7
(v)
23
5
Question
18
18.
Find the difference between the values of numbers at point A and B
(i)
(
-3
10
)
(ii)
(
-1
12
)
(iii)
(
-1
10
)
(iv)
1
10
(v)
(
-1
8
)
Question
19
19.
Rationalise the denominator of
(
3
√
5
+
3
√
7
)
(
√
2
+
5
√
3
)
=
(i)
(
−
3
73
√
10
−
3
73
√
14
+
15
73
√
15
+
15
73
√
23
)
(ii)
(
−
3
73
√
10
−
3
73
√
14
+
15
73
4
√
15
+
15
73
√
21
)
(iii)
(
−
3
73
√
10
−
3
73
√
14
+
15
73
√
15
+
15
73
√
21
)
(iv)
(
−
3
73
√
10
−
3
73
4
√
14
+
15
73
√
15
+
15
73
√
21
)
(v)
(
−
3
73
√
7
−
3
73
√
14
+
15
73
√
15
+
15
73
√
21
)
Question
20
20.
Which of the following are true?
a)
real numbers are closed under subtraction
b)
real numbers are closed under addition
c)
real numbers are closed under multiplication
d)
real numbers are closed under division
(i)
{d,b}
(ii)
{a,b,c}
(iii)
{d,a,b}
(iv)
{d,a}
(v)
{d,c}
Question
21
21.
Which of the following are true?
a)
13
12
+
(
78
17
+
7
3
)
=
(
13
12
+
78
17
)
+
7
3
b)
13
12
✕
(
132
13
✕
18
13
)
=
(
13
12
✕
132
13
)
✕
18
13
c)
1
10
÷
(
132
13
÷
1
14
)
=
(
1
10
÷
132
13
)
÷
1
14
d)
1
10
−
(
78
17
−
11
13
)
=
(
1
10
−
78
17
)
−
11
13
(i)
{c,a}
(ii)
{a,b}
(iii)
{c,b,a}
(iv)
{d,b}
(v)
{c,d,a}
Question
22
22.
Rationalise the denominator of
(
−
√
5
+
√
7
)
(
√
2
−
√
5
)
=
(i)
(
1
3
√
10
−
1
3
√
14
+
5
3
−
1
3
√
38
)
(ii)
(
1
3
√
7
−
1
3
√
14
+
5
3
−
1
3
√
35
)
(iii)
(
1
3
√
10
−
1
3
4
√
14
+
5
3
−
1
3
√
35
)
(iv)
(
1
3
√
10
−
1
3
√
14
+
5
3
−
1
3
√
35
)
(v)
(
1
3
√
10
−
1
3
√
14
+
7
5
−
1
3
√
35
)
Question
23
23.
Which of the following are true?
a)
1
13
÷
(
31
20
+
3
7
)
=
(
1
13
÷
31
20
)
+
(
1
13
÷
3
7
)
b)
17
2
✕
(
89
15
−
1
19
)
=
(
17
2
✕
89
15
)
−
(
17
2
✕
1
19
)
c)
17
2
✕
(
31
20
+
19
20
)
=
(
17
2
✕
31
20
)
+
(
17
2
✕
19
20
)
d)
1
13
−
(
89
15
✕
2
13
)
=
(
1
13
−
89
15
)
✕
(
1
13
−
2
13
)
(i)
{a,c,b}
(ii)
{d,c}
(iii)
{b,c}
(iv)
{a,b}
(v)
{a,d,b}
Question
24
24.
Find the sum of the rational numbers at the points labelled with letters N and O
(i)
(
-97
8
)
(ii)
(
-121
10
)
(iii)
(
-117
10
)
(iv)
(
-119
10
)
(v)
(
-47
4
)
Question
25
25.
Find the sum of the rational numbers at the points labelled with letters N and O
(i)
37
2
(ii)
183
10
(iii)
73
4
(iv)
181
10
(v)
147
8
Assignment Key
1) (v)
2) (iii)
3) (ii)
4) (v)
5) (ii)
6) (i)
7) (iv)
8) (iii)
9) (ii)
10) (i)
11) (v)
12) (i)
13) (i)
14) (iii)
15) (i)
16) (v)
17) (i)
18) (iii)
19) (iii)
20) (ii)
21) (ii)
22) (iv)
23) (iii)
24) (iv)
25) (ii)
