EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
The rationalising factor of
(
−
4
√
9
+
3
√
7
)
=
(i)
(
−
12
−
21
)
(ii)
(
−
12
−
3
√
7
)
(iii)
(
−
10
−
3
√
7
)
(iv)
(
−
14
−
3
√
7
)
(v)
(
−
12
−
3
4
√
7
)
Question
2
2.
Which of the following are true?
a)
1
16
✕
23
5
=
23
5
✕
1
16
b)
7
9
−
29
2
=
29
2
−
7
9
c)
1
16
+
29
2
=
29
2
+
1
16
d)
7
9
÷
23
5
=
23
5
÷
7
9
(i)
{b,d,a}
(ii)
{b,c,a}
(iii)
{b,a}
(iv)
{d,c}
(v)
{a,c}
Question
3
3.
Find the sum of the rational numbers at the points labelled with letters I and J
(i)
53
5
(ii)
51
5
(iii)
11
(iv)
73
7
Question
4
4.
Find the difference of the rational numbers at the points labelled with letters H and I
(i)
(
-3
10
)
(ii)
(
-1
4
)
(iii)
(
-1
10
)
(iv)
(
-3
8
)
(v)
(
-1
2
)
Question
5
5.
Find the rational number at the point labelled with letter R
(i)
13
8
(ii)
11
6
(iii)
13
6
(iv)
5
2
(v)
13
4
Question
6
6.
Rationalise the denominator of
(
√
6
−
√
4
)
(
√
3
−
√
2
)
=
(i)
√
2
(ii)
4
√
2
(iii)
2
(iv)
√
-1
(v)
√
4
Question
7
7.
Which of the following are true?
a)
1
14
−
(
169
18
✕
13
6
)
=
(
1
14
−
169
18
)
✕
(
1
14
−
13
6
)
b)
19
20
✕
(
169
18
−
12
11
)
=
(
19
20
✕
169
18
)
−
(
19
20
✕
12
11
)
c)
19
20
✕
(
39
10
+
7
20
)
=
(
19
20
✕
39
10
)
+
(
19
20
✕
7
20
)
d)
1
14
÷
(
39
10
+
8
11
)
=
(
1
14
÷
39
10
)
+
(
1
14
÷
8
11
)
(i)
{a,b}
(ii)
{a,c,b}
(iii)
{b,c}
(iv)
{d,c}
(v)
{a,d,b}
Question
8
8.
Which of the following are true?
a)
11
4
+
(
29
5
+
5
4
)
=
(
11
4
+
29
5
)
+
5
4
b)
11
4
✕
(
16
5
✕
9
2
)
=
(
11
4
✕
16
5
)
✕
9
2
c)
14
5
÷
(
16
5
÷
16
13
)
=
(
14
5
÷
16
5
)
÷
16
13
d)
14
5
−
(
29
5
−
11
3
)
=
(
14
5
−
29
5
)
−
11
3
(i)
{d,b}
(ii)
{c,b,a}
(iii)
{c,d,a}
(iv)
{a,b}
(v)
{c,a}
Question
9
9.
Find the product of the rational numbers at the points labelled with letters Q and R
(i)
36
5
(ii)
50
7
(iii)
22
3
(iv)
38
5
(v)
34
5
Question
10
10.
Rationalise the denominator of
1
(
√
2
−
2
√
6
)
(i)
(
−
1
22
√
-1
−
1
11
√
6
)
(ii)
(
−
1
22
√
2
−
1
11
√
6
)
(iii)
(
−
1
22
√
5
−
1
11
√
6
)
(iv)
(
−
1
22
√
2
−
1
11
4
√
6
)
(v)
(
−
1
22
√
2
−
6
11
)
Question
11
11.
Find the rational number at the point labelled with letter J
(i)
(
-22
3
)
(ii)
-4
(iii)
(
-22
7
)
(iv)
(
-24
5
)
(v)
(
-22
5
)
Question
12
12.
Find the product of the rational numbers at the points labelled with letters I and J
(i)
143
5
(ii)
29
(iii)
141
5
(iv)
199
7
Question
13
13.
Which of the following is an irrational number?
(i)
12
(ii)
1
(iii)
13
24
(iv)
3
√
50
(v)
14.5238
Question
14
14.
Find the position of the rational number
29
8
on the number line
(i)
E
(ii)
G
(iii)
N
(iv)
R
(v)
Q
Question
15
15.
Rationalise the denominator of
1
(
−
√
4
+
√
8
)
(i)
(
1
2
+
1
2
√
2
)
(ii)
(
−
1
2
+
1
2
√
2
)
(iii)
(
1
2
+
1
2
4
√
2
)
(iv)
(
1
2
+
1
)
(v)
(
3
2
+
1
2
√
2
)
Question
16
16.
Rationalise the denominator of
(
√
6
−
2
√
2
)
(
5
√
3
+
4
√
5
)
=
(i)
(
−
√
15
+
2
√
6
+
4
5
√
30
−
8
5
√
10
)
(ii)
(
−
√
18
+
2
√
6
+
4
5
√
30
−
8
5
√
12
)
(iii)
(
−
√
18
+
2
4
√
6
+
4
5
√
30
−
8
5
√
10
)
(iv)
(
−
√
18
+
2
√
6
+
4
5
√
30
−
8
5
√
10
)
(v)
(
−
√
18
+
2
√
6
+
4
5
4
√
30
−
8
5
√
10
)
Question
17
17.
Which of the following is a rational number?
(i)
√
98
(ii)
3
√
97
(iii)
3
√
56
(iv)
√
75
(v)
1
3
Question
18
18.
Which of the following are true?
a)
real numbers are closed under subtraction
b)
real numbers are closed under division
c)
real numbers are closed under multiplication
d)
real numbers are closed under addition
(i)
{b,d}
(ii)
{a,c,d}
(iii)
{b,a,c}
(iv)
{b,a}
(v)
{b,c}
Question
19
19.
Rationalise the denominator of
1
6
√
6
(i)
1
36
4
√
6
(ii)
1
6
(iii)
1
36
√
3
(iv)
1
36
√
8
(v)
1
36
√
6
Question
20
20.
Find the sum of the rational numbers at the points labelled with letters I and J
(i)
(
-103
10
)
(ii)
(
-81
8
)
(iii)
(
-101
10
)
(iv)
(
-99
10
)
(v)
(
-121
12
)
Question
21
21.
The rationalising factor of
(
−
6
√
62
)
=
(i)
√
62
(ii)
62
(iii)
4
√
62
(iv)
√
59
(v)
√
64
Question
22
22.
Find the difference of the rational numbers at the points labelled with letters K and L
(i)
(
-3
5
)
(ii)
(
-1
5
)
(iii)
1
5
(iv)
(
-1
3
)
(v)
(
-1
7
)
Question
23
23.
Find the difference between the values of numbers at point A and B
(i)
11
17
(ii)
3
5
(iii)
11
13
(iv)
13
15
(v)
11
15
Question
24
24.
Find the position of the rational number
(
-19
3
)
on the number line
(i)
N
(ii)
O
(iii)
E
(iv)
I
(v)
F
Question
25
25.
Which of the following are true?
a)
rational numbers are closed under subtraction
b)
rational numbers are closed under multiplication
c)
rational numbers are closed under division
d)
rational numbers are closed under addition
(i)
{a,b,d}
(ii)
{c,a,b}
(iii)
{c,d}
(iv)
{c,a}
(v)
{c,b}
Assignment Key
1) (ii)
2) (v)
3) (i)
4) (i)
5) (iii)
6) (i)
7) (iii)
8) (iv)
9) (i)
10) (ii)
11) (v)
12) (i)
13) (iv)
14) (v)
15) (i)
16) (iv)
17) (v)
18) (ii)
19) (v)
20) (iii)
21) (i)
22) (ii)
23) (v)
24) (ii)
25) (i)
