EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Which of the following is a rational number?
(i)
14
17
(ii)
√
66
(iii)
3
√
58
(iv)
√
56
(v)
√
61
Question
2
2.
Which of the following are true?
a)
11
16
✕
(
51
5
−
5
4
)
=
(
11
16
✕
51
5
)
−
(
11
16
✕
5
4
)
b)
11
16
✕
(
154
17
+
3
11
)
=
(
11
16
✕
154
17
)
+
(
11
16
✕
3
11
)
c)
17
14
−
(
51
5
✕
16
11
)
=
(
17
14
−
51
5
)
✕
(
17
14
−
16
11
)
d)
17
14
÷
(
154
17
+
8
11
)
=
(
17
14
÷
154
17
)
+
(
17
14
÷
8
11
)
(i)
{a,b}
(ii)
{c,d,a}
(iii)
{c,a}
(iv)
{c,b,a}
(v)
{d,b}
Question
3
3.
Which of the following are true?
a)
real numbers are closed under multiplication
b)
real numbers are closed under subtraction
c)
real numbers are closed under addition
d)
real numbers are closed under division
(i)
{d,b}
(ii)
{d,a,b}
(iii)
{d,a}
(iv)
{a,b,c}
(v)
{d,c}
Question
4
4.
Rationalise the denominator of
1
5
√
2
(i)
1
10
√
2
(ii)
1
10
√
4
(iii)
1
5
(iv)
1
10
4
√
2
(v)
1
10
√
1
2
Question
5
5.
Find the product of the rational numbers at the points labelled with letters S and T
(i)
166
9
(ii)
426
23
(iii)
92
5
(iv)
462
25
(v)
464
25
Question
6
6.
The rationalising factor of
8
√
81
=
(i)
0
(ii)
(
−
2
)
(iii)
1
(iv)
3
(v)
2
Question
7
7.
Which of the following are true?
a)
4
7
✕
154
17
=
154
17
✕
4
7
b)
4
7
+
137
18
=
137
18
+
4
7
c)
9
5
÷
154
17
=
154
17
÷
9
5
d)
9
5
−
137
18
=
137
18
−
9
5
(i)
{a,b}
(ii)
{d,b}
(iii)
{c,d,a}
(iv)
{c,b,a}
(v)
{c,a}
Question
8
8.
Find the difference of the rational numbers at the points labelled with letters J and K
(i)
(
-7
12
)
(ii)
(
-7
10
)
(iii)
(
-1
2
)
(iv)
(
-9
10
)
(v)
(
-7
8
)
Question
9
9.
Find the sum of the rational numbers at the points labelled with letters D and E
(i)
73
10
(ii)
71
10
(iii)
59
8
(iv)
29
4
(v)
15
2
Question
10
10.
Rationalise the denominator of
(
2
√
6
+
5
√
5
)
(
√
6
+
4
√
4
)
=
(i)
(
−
6
29
−
5
58
√
30
+
8
29
4
√
6
+
20
29
√
5
)
(ii)
(
−
6
29
−
5
58
√
30
+
8
29
√
6
+
20
29
√
8
)
(iii)
(
−
6
29
−
5
58
4
√
30
+
8
29
√
6
+
20
29
√
5
)
(iv)
(
−
8
29
−
5
58
√
30
+
8
29
√
6
+
20
29
√
5
)
(v)
(
−
6
29
−
5
58
√
30
+
8
29
√
6
+
20
29
√
5
)
Question
11
11.
Which of the following is an irrational number?
(i)
1
(ii)
12.619
(iii)
27
(iv)
1
12
(v)
√
27
Question
12
12.
Find the sum of the rational numbers at the points labelled with letters I and J
(i)
(
-87
7
)
(ii)
(
-63
5
)
(iii)
(
-61
5
)
(iv)
-13
Question
13
13.
Find the rational number at the point labelled with letter D
(i)
-6
(ii)
(
-34
5
)
(iii)
(
-32
3
)
(iv)
(
-32
7
)
(v)
(
-32
5
)
Question
14
14.
The rationalising factor of
(
5
√
6
−
3
√
5
)
=
(i)
(
5
√
6
+
3
4
√
5
)
(ii)
(
5
√
6
+
3
√
5
)
(iii)
(
5
√
3
+
3
√
5
)
(iv)
(
5
√
6
+
15
)
(v)
(
5
√
9
+
3
√
5
)
Question
15
15.
Find the difference between the values of numbers at point A and B
(i)
(
-4
5
)
(ii)
(
-2
3
)
(iii)
0
(iv)
(
-2
7
)
(v)
(
-2
5
)
Question
16
16.
Find the position of the rational number
(
-16
3
)
on the number line
(i)
F
(ii)
P
(iii)
Q
(iv)
J
(v)
H
Question
17
17.
Find the difference of the rational numbers at the points labelled with letters I and J
(i)
0
(ii)
(
-2
7
)
(iii)
(
-2
5
)
(iv)
(
-4
5
)
(v)
(
-2
3
)
Question
18
18.
Rationalise the denominator of
1
(
−
√
6
+
√
7
)
(i)
(
√
6
+
4
√
7
)
(ii)
(
√
6
+
√
7
)
(iii)
(
√
8
+
√
7
)
(iv)
(
√
6
+
7
)
(v)
(
√
4
+
√
7
)
Question
19
19.
Which of the following are true?
a)
20
17
✕
(
37
6
✕
6
13
)
=
(
20
17
✕
37
6
)
✕
6
13
b)
16
15
−
(
35
16
−
15
8
)
=
(
16
15
−
35
16
)
−
15
8
c)
20
17
+
(
35
16
+
11
12
)
=
(
20
17
+
35
16
)
+
11
12
d)
16
15
÷
(
37
6
÷
14
15
)
=
(
16
15
÷
37
6
)
÷
14
15
(i)
{b,d,a}
(ii)
{d,c}
(iii)
{b,c,a}
(iv)
{b,a}
(v)
{a,c}
Question
20
20.
Find the position of the rational number
16
3
on the number line
(i)
O
(ii)
R
(iii)
L
(iv)
N
(v)
D
Question
21
21.
Find the rational number at the point labelled with letter D
(i)
46
5
(ii)
48
5
(iii)
46
3
(iv)
44
5
(v)
46
7
Question
22
22.
Find the product of the rational numbers at the points labelled with letters Q and R
(i)
1388
25
(ii)
1276
23
(iii)
1386
25
(iv)
1384
25
(v)
1496
27
Question
23
23.
Rationalise the denominator of
1
(
7
√
9
+
4
√
8
)
(i)
(
21
313
−
16
313
)
(ii)
(
23
313
−
8
313
√
2
)
(iii)
(
21
313
−
8
313
4
√
2
)
(iv)
(
21
313
−
8
313
√
2
)
(v)
(
19
313
−
8
313
√
2
)
Question
24
24.
Which of the following are true?
a)
rational numbers are closed under subtraction
b)
rational numbers are closed under addition
c)
rational numbers are closed under multiplication
d)
rational numbers are closed under division
(i)
{a,b,c}
(ii)
{d,c}
(iii)
{d,b}
(iv)
{d,a}
(v)
{d,a,b}
Question
25
25.
Rationalise the denominator of
(
√
3
+
√
6
)
0
=
(i)
(
√
3
+
√
6
)
(ii)
(
√
1
3
+
√
6
)
(iii)
(
√
3
+
6
)
(iv)
(
√
3
+
4
√
6
)
(v)
(
√
6
+
√
6
)
Assignment Key
1) (i)
2) (i)
3) (iv)
4) (i)
5) (iv)
6) (iii)
7) (i)
8) (ii)
9) (i)
10) (v)
11) (v)
12) (ii)
13) (v)
14) (ii)
15) (v)
16) (iv)
17) (iii)
18) (ii)
19) (v)
20) (iii)
21) (i)
22) (iii)
23) (iv)
24) (i)
25) (i)
