EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Find the sum of the rational numbers at the points labelled with letters D and E
(i)
79
10
(ii)
97
12
(iii)
65
8
(iv)
81
10
(v)
83
10
Question
2
2.
The rationalising factor of
3
√
81
=
(i)
2
(ii)
(
−
1
)
(iii)
1
(iv)
0
(v)
3
Question
3
3.
Find the difference of the rational numbers at the points labelled with letters M and N
(i)
(
-3
10
)
(ii)
(
-1
2
)
(iii)
(
-3
8
)
(iv)
(
-1
4
)
(v)
(
-1
10
)
Question
4
4.
Rationalise the denominator of
1
(
2
√
8
−
√
4
)
(i)
(
1
7
√
2
+
1
14
)
(ii)
(
1
7
√
2
+
1
16
)
(iii)
(
1
7
√
-1
+
1
14
)
(iv)
(
1
7
√
5
+
1
14
)
(v)
(
1
7
√
2
+
1
12
)
Question
5
5.
Find the position of the rational number
(
-38
5
)
on the number line
(i)
Q
(ii)
G
(iii)
I
(iv)
K
(v)
P
Question
6
6.
Find the difference of the rational numbers at the points labelled with letters M and N
(i)
1
5
(ii)
(
-1
3
)
(iii)
(
-1
5
)
(iv)
(
-3
5
)
(v)
(
-1
7
)
Question
7
7.
Find the product of the rational numbers at the points labelled with letters I and J
(i)
1583
20
(ii)
7917
100
(iii)
475
6
(iv)
7919
100
(v)
7759
98
Question
8
8.
The rationalising factor of
(
−
5
√
8
+
7
√
7
)
=
(i)
(
−
10
√
2
−
7
4
√
7
)
(ii)
(
−
10
√
2
−
49
)
(iii)
(
−
10
√
2
−
7
√
7
)
(iv)
(
−
10
√
5
−
7
√
7
)
(v)
(
−
10
√
-1
−
7
√
7
)
Question
9
9.
Which of the following are true?
a)
rational numbers are closed under multiplication
b)
rational numbers are closed under division
c)
rational numbers are closed under addition
d)
rational numbers are closed under subtraction
(i)
{b,a,c}
(ii)
{b,d}
(iii)
{a,c,d}
(iv)
{b,c}
(v)
{b,a}
Question
10
10.
Rationalise the denominator of
1
(
−
√
7
+
√
6
)
(i)
(
−
√
7
−
√
6
)
(ii)
(
−
√
7
−
4
√
6
)
(iii)
(
−
√
7
−
6
)
(iv)
(
−
√
4
−
√
6
)
(v)
(
−
√
10
−
√
6
)
Question
11
11.
Rationalise the denominator of
1
(
−
7
√
6
)
(i)
(
−
1
42
√
6
)
(ii)
(
−
1
42
√
9
)
(iii)
(
−
1
42
4
√
6
)
(iv)
(
−
1
42
√
3
)
(v)
(
−
1
7
)
Question
12
12.
Find the rational number at the point labelled with letter J
(i)
(
-51
7
)
(ii)
-7
(iii)
(
-53
7
)
(iv)
(
-51
5
)
(v)
(
-17
3
)
Question
13
13.
Find the rational number at the point labelled with letter H
(i)
25
9
(ii)
23
7
(iii)
27
7
(iv)
25
7
(v)
5
Question
14
14.
Find the difference between the values of numbers at point A and B
(i)
4
9
(ii)
6
7
(iii)
4
5
(iv)
4
7
(v)
2
7
Question
15
15.
Which of the following are true?
a)
19
20
−
(
118
13
−
9
11
)
=
(
19
20
−
118
13
)
−
9
11
b)
15
13
+
(
118
13
+
15
7
)
=
(
15
13
+
118
13
)
+
15
7
c)
15
13
✕
(
49
12
✕
5
16
)
=
(
15
13
✕
49
12
)
✕
5
16
d)
19
20
÷
(
49
12
÷
13
19
)
=
(
19
20
÷
49
12
)
÷
13
19
(i)
{a,d,b}
(ii)
{d,c}
(iii)
{a,b}
(iv)
{a,c,b}
(v)
{b,c}
Question
16
16.
Rationalise the denominator of
(
√
7
+
√
9
)
(
√
3
+
√
7
)
=
(i)
(
−
1
4
√
21
−
3
4
√
3
+
3
2
+
3
4
√
7
)
(ii)
(
−
1
4
√
21
−
3
4
4
√
3
+
7
4
+
3
4
√
7
)
(iii)
(
−
1
4
√
21
−
3
4
√
3
+
7
4
+
3
4
√
10
)
(iv)
(
−
1
4
√
19
−
3
4
√
3
+
7
4
+
3
4
√
7
)
(v)
(
−
1
4
√
21
−
3
4
√
3
+
7
4
+
3
4
√
7
)
Question
17
17.
Find the product of the rational numbers at the points labelled with letters M and N
(i)
744
25
(ii)
684
23
(iii)
148
5
(iv)
800
27
(v)
742
25
Question
18
18.
Which of the following are true?
a)
15
19
÷
(
74
11
+
14
11
)
=
(
15
19
÷
74
11
)
+
(
15
19
÷
14
11
)
b)
19
18
✕
(
74
11
+
1
9
)
=
(
19
18
✕
74
11
)
+
(
19
18
✕
1
9
)
c)
19
18
✕
(
11
2
−
9
14
)
=
(
19
18
✕
11
2
)
−
(
19
18
✕
9
14
)
d)
15
19
−
(
11
2
✕
16
17
)
=
(
15
19
−
11
2
)
✕
(
15
19
−
16
17
)
(i)
{b,c}
(ii)
{a,b}
(iii)
{a,d,b}
(iv)
{a,c,b}
(v)
{d,c}
Question
19
19.
Which of the following is a rational number?
(i)
3
√
30
(ii)
5
11
(iii)
3
√
42
(iv)
√
42
(v)
√
18
Question
20
20.
Which of the following are true?
a)
14
3
÷
122
13
=
122
13
÷
14
3
b)
14
3
−
121
15
=
121
15
−
14
3
c)
19
18
✕
122
13
=
122
13
✕
19
18
d)
19
18
+
121
15
=
121
15
+
19
18
(i)
{a,c}
(ii)
{a,b,c}
(iii)
{a,d,c}
(iv)
{c,d}
(v)
{b,d}
Question
21
21.
Which of the following are true?
a)
real numbers are closed under multiplication
b)
real numbers are closed under addition
c)
real numbers are closed under subtraction
d)
real numbers are closed under division
(i)
{d,b}
(ii)
{d,c}
(iii)
{a,b,c}
(iv)
{d,a}
(v)
{d,a,b}
Question
22
22.
Find the position of the rational number
11
2
on the number line
(i)
R
(ii)
I
(iii)
N
(iv)
E
(v)
M
Question
23
23.
Find the sum of the rational numbers at the points labelled with letters I and J
(i)
(
-171
10
)
(ii)
(
-167
10
)
(iii)
(
-67
4
)
(iv)
(
-137
8
)
(v)
(
-169
10
)
Question
24
24.
Which of the following is an irrational number?
(i)
3
√
21
(ii)
1
2
(iii)
7
(iv)
26
(v)
8.9444
Question
25
25.
Rationalise the denominator of
(
√
6
+
5
√
8
)
(
2
√
8
−
2
√
3
)
=
(i)
(
1
5
√
10
+
4
+
1
10
√
18
+
√
6
)
(ii)
(
1
5
√
12
+
4
+
1
10
√
18
+
√
6
)
(iii)
(
1
5
√
12
+
5
+
1
10
√
18
+
√
6
)
(iv)
(
1
5
√
12
+
4
+
1
10
4
√
18
+
√
6
)
(v)
(
1
5
√
12
+
4
+
1
10
√
18
+
√
9
)
Assignment Key
1) (iv)
2) (iii)
3) (i)
4) (i)
5) (iv)
6) (iii)
7) (ii)
8) (iii)
9) (iii)
10) (i)
11) (i)
12) (i)
13) (iv)
14) (iv)
15) (v)
16) (v)
17) (v)
18) (i)
19) (ii)
20) (iv)
21) (iii)
22) (ii)
23) (v)
24) (i)
25) (ii)
