EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
20
9
✕
(
28
9
+
4
3
)
=
(
20
9
✕
28
9
)
+
(
20
9
✕
4
3
)
b)
13
20
÷
(
28
9
+
17
20
)
=
(
13
20
÷
28
9
)
+
(
13
20
÷
17
20
)
c)
20
9
✕
(
8
3
−
13
8
)
=
(
20
9
✕
8
3
)
−
(
20
9
✕
13
8
)
d)
13
20
−
(
8
3
✕
15
7
)
=
(
13
20
−
8
3
)
✕
(
13
20
−
15
7
)
(i)
{b,d,a}
(ii)
{b,a}
(iii)
{a,c}
(iv)
{b,c,a}
(v)
{d,c}
Question
2
2.
Rationalise the denominator of
1
(
√
2
−
√
7
)
(i)
(
−
1
5
√
2
−
7
5
)
(ii)
(
−
1
5
√
5
−
1
5
√
7
)
(iii)
(
−
1
5
√
2
−
1
5
4
√
7
)
(iv)
(
−
1
5
√
1
2
−
1
5
√
7
)
(v)
(
−
1
5
√
2
−
1
5
√
7
)
Question
3
3.
Find the difference of the rational numbers at the points labelled with letters F and G
(i)
(
-1
2
)
(ii)
(
-1
10
)
(iii)
(
-3
10
)
(iv)
(
-3
8
)
(v)
(
-1
4
)
Question
4
4.
Find the sum of the rational numbers at the points labelled with letters K and L
(i)
(
-145
12
)
(ii)
(
-119
10
)
(iii)
(
-121
10
)
(iv)
(
-97
8
)
(v)
(
-123
10
)
Question
5
5.
Find the difference of the rational numbers at the points labelled with letters D and E
(i)
(
-9
10
)
(ii)
(
-1
2
)
(iii)
(
-7
8
)
(iv)
(
-7
10
)
(v)
(
-7
12
)
Question
6
6.
Find the rational number at the point labelled with letter R
(i)
(
-36
7
)
(ii)
(
-34
7
)
(iii)
(
-34
5
)
(iv)
(
-32
7
)
(v)
(
-34
9
)
Question
7
7.
Rationalise the denominator of
1
(
6
√
8
−
6
√
6
)
(i)
(
1
6
√
-1
+
1
12
√
6
)
(ii)
(
1
6
√
5
+
1
12
√
6
)
(iii)
(
1
6
√
2
+
1
12
√
6
)
(iv)
(
1
6
√
2
+
1
12
4
√
6
)
(v)
(
1
6
√
2
+
1
2
)
Question
8
8.
Find the difference between the values of numbers at point A and B
(i)
4
9
(ii)
4
7
(iii)
2
3
(iv)
4
11
(v)
2
9
Question
9
9.
Which of the following are true?
a)
real numbers are closed under subtraction
b)
real numbers are closed under multiplication
c)
real numbers are closed under division
d)
real numbers are closed under addition
(i)
{c,a,b}
(ii)
{c,a}
(iii)
{a,b,d}
(iv)
{c,b}
(v)
{c,d}
Question
10
10.
The rationalising factor of
2
√
68
=
(i)
√
19
(ii)
4
√
17
(iii)
√
14
(iv)
√
17
(v)
17
Question
11
11.
Find the product of the rational numbers at the points labelled with letters Q and R
(i)
84
5
(ii)
120
7
(iii)
88
5
(iv)
86
5
(v)
52
3
Question
12
12.
Find the position of the rational number
(
-19
3
)
on the number line
(i)
R
(ii)
L
(iii)
G
(iv)
H
(v)
O
Question
13
13.
Which of the following are true?
a)
rational numbers are closed under addition
b)
rational numbers are closed under multiplication
c)
rational numbers are closed under division
d)
rational numbers are closed under subtraction
(i)
{c,d}
(ii)
{c,b}
(iii)
{c,a}
(iv)
{c,a,b}
(v)
{a,b,d}
Question
14
14.
Which of the following are true?
a)
15
19
✕
41
3
=
41
3
✕
15
19
b)
15
19
+
59
6
=
59
6
+
15
19
c)
1
10
÷
41
3
=
41
3
÷
1
10
d)
1
10
−
59
6
=
59
6
−
1
10
(i)
{c,a}
(ii)
{c,b,a}
(iii)
{a,b}
(iv)
{c,d,a}
(v)
{d,b}
Question
15
15.
Find the sum of the rational numbers at the points labelled with letters E and F
(i)
151
10
(ii)
121
8
(iii)
59
4
(iv)
147
10
(v)
149
10
Question
16
16.
Find the product of the rational numbers at the points labelled with letters J and K
(i)
2411
50
(ii)
771
16
(iii)
2407
50
(iv)
2409
50
(v)
2505
52
Question
17
17.
Rationalise the denominator of
(
−
√
9
+
√
7
)
(
√
3
−
√
8
)
=
(i)
(
3
5
√
3
−
1
5
√
21
+
6
5
4
√
2
−
2
5
√
14
)
(ii)
(
3
5
√
3
−
1
5
√
21
+
6
5
√
2
−
2
5
√
16
)
(iii)
(
3
5
√
3
−
1
5
4
√
21
+
6
5
√
2
−
2
5
√
14
)
(iv)
(
3
5
√
3
−
1
5
√
21
+
6
5
√
2
−
2
5
√
14
)
(v)
(
3
5
−
1
5
√
21
+
6
5
√
2
−
2
5
√
14
)
Question
18
18.
Rationalise the denominator of
(
√
6
−
4
√
7
)
(
−
3
√
5
+
√
2
)
=
(i)
(
−
3
43
√
30
+
12
43
√
35
−
1
43
√
12
+
4
43
√
17
)
(ii)
(
−
3
43
√
30
+
12
43
√
35
−
1
43
4
√
12
+
4
43
√
14
)
(iii)
(
−
3
43
√
27
+
12
43
√
35
−
1
43
√
12
+
4
43
√
14
)
(iv)
(
−
3
43
√
30
+
12
43
4
√
35
−
1
43
√
12
+
4
43
√
14
)
(v)
(
−
3
43
√
30
+
12
43
√
35
−
1
43
√
12
+
4
43
√
14
)
Question
19
19.
Which of the following is an irrational number?
(i)
26.6111
(ii)
(-9)
(iii)
18
(iv)
3
√
32
(v)
2
4
Question
20
20.
The rationalising factor of
(
−
3
√
7
−
8
√
9
)
=
(i)
(
−
3
√
10
+
24
)
(ii)
(
−
3
√
7
+
23
)
(iii)
(
−
3
√
7
+
25
)
(iv)
(
−
3
√
4
+
24
)
(v)
(
−
3
√
7
+
24
)
Question
21
21.
Find the rational number at the point labelled with letter P
(i)
38
9
(ii)
40
11
(iii)
40
9
(iv)
14
3
(v)
40
7
Question
22
22.
Which of the following are true?
a)
2
17
−
(
120
17
−
10
7
)
=
(
2
17
−
120
17
)
−
10
7
b)
2
17
÷
(
47
14
÷
7
19
)
=
(
2
17
÷
47
14
)
÷
7
19
c)
6
7
✕
(
47
14
✕
4
17
)
=
(
6
7
✕
47
14
)
✕
4
17
d)
6
7
+
(
120
17
+
7
12
)
=
(
6
7
+
120
17
)
+
7
12
(i)
{b,d}
(ii)
{a,d,c}
(iii)
{c,d}
(iv)
{a,b,c}
(v)
{a,c}
Question
23
23.
Rationalise the denominator of
1
(
−
8
√
2
)
(i)
(
−
1
16
√
-1
)
(ii)
(
−
1
16
√
2
)
(iii)
(
−
1
16
√
5
)
(iv)
(
−
1
16
4
√
2
)
(v)
(
−
1
8
)
Question
24
24.
Find the position of the rational number
15
7
on the number line
(i)
E
(ii)
Q
(iii)
H
(iv)
F
(v)
K
Question
25
25.
Which of the following is a rational number?
(i)
√
79
(ii)
√
63
(iii)
2
23
(iv)
3
√
98
(v)
√
89
Assignment Key
1) (iii)
2) (v)
3) (iii)
4) (iii)
5) (iv)
6) (ii)
7) (iii)
8) (i)
9) (iii)
10) (iv)
11) (iv)
12) (iv)
13) (v)
14) (iii)
15) (v)
16) (iv)
17) (iv)
18) (v)
19) (iv)
20) (v)
21) (iii)
22) (iii)
23) (ii)
24) (iii)
25) (iii)
