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 M
(i)
43
9
(ii)
41
9
(iii)
43
7
(iv)
43
11
(v)
5
Question
2
2.
Rationalise the denominator of
1
(
2
√
3
−
3
√
6
)
(i)
(
−
1
21
√
3
−
1
14
4
√
6
)
(ii)
(
−
1
21
√
6
−
1
14
√
6
)
(iii)
(
−
1
21
√
3
−
3
7
)
(iv)
(
−
1
21
−
1
14
√
6
)
(v)
(
−
1
21
√
3
−
1
14
√
6
)
Question
3
3.
The rationalising factor of
(
−
27
−
6
√
3
)
=
(i)
(
−
30
+
6
√
3
)
(ii)
(
−
27
+
18
)
(iii)
(
−
27
+
6
4
√
3
)
(iv)
(
−
25
+
6
√
3
)
(v)
(
−
27
+
6
√
3
)
Question
4
4.
Rationalise the denominator of
1
(
−
4
√
8
)
(i)
(
−
1
16
√
5
)
(ii)
(
−
1
16
√
2
)
(iii)
(
−
1
8
)
(iv)
(
−
1
16
√
1
2
)
(v)
(
−
1
16
4
√
2
)
Question
5
5.
Rationalise the denominator of
1
(
−
2
√
2
−
√
6
)
(i)
(
−
√
-1
+
1
2
√
6
)
(ii)
(
−
√
4
+
1
2
√
6
)
(iii)
(
−
√
2
+
1
2
√
6
)
(iv)
(
−
√
2
+
1
2
4
√
6
)
(v)
(
−
√
2
+
3
)
Question
6
6.
Find the sum of the rational numbers at the points labelled with letters H and I
(i)
77
4
(ii)
20
(iii)
39
2
(iv)
37
2
(v)
41
2
Question
7
7.
Which of the following are true?
a)
1
3
÷
29
3
=
29
3
÷
1
3
b)
1
3
−
13
4
=
13
4
−
1
3
c)
1
10
✕
29
3
=
29
3
✕
1
10
d)
1
10
+
13
4
=
13
4
+
1
10
(i)
{a,c}
(ii)
{a,d,c}
(iii)
{a,b,c}
(iv)
{c,d}
(v)
{b,d}
Question
8
8.
Which of the following are true?
a)
rational numbers are closed under division
b)
rational numbers are closed under addition
c)
rational numbers are closed under subtraction
d)
rational numbers are closed under multiplication
(i)
{a,b}
(ii)
{a,d}
(iii)
{b,c,d}
(iv)
{a,c}
(v)
{a,b,c}
Question
9
9.
The rationalising factor of
3
√
83
=
(i)
√
86
(ii)
√
80
(iii)
83
(iv)
√
83
(v)
4
√
83
Question
10
10.
Find the position of the rational number
16
3
on the number line
(i)
P
(ii)
E
(iii)
I
(iv)
J
(v)
D
Question
11
11.
Which of the following are true?
a)
7
20
✕
(
34
7
✕
14
19
)
=
(
7
20
✕
34
7
)
✕
14
19
b)
10
11
−
(
79
16
−
3
19
)
=
(
10
11
−
79
16
)
−
3
19
c)
7
20
+
(
79
16
+
13
18
)
=
(
7
20
+
79
16
)
+
13
18
d)
10
11
÷
(
34
7
÷
3
19
)
=
(
10
11
÷
34
7
)
÷
3
19
(i)
{d,c}
(ii)
{a,c}
(iii)
{b,c,a}
(iv)
{b,a}
(v)
{b,d,a}
Question
12
12.
Find the position of the rational number
(
-38
5
)
on the number line
(i)
K
(ii)
N
(iii)
F
(iv)
E
(v)
I
Question
13
13.
Which of the following is an irrational number?
(i)
21
(ii)
3
√
73
(iii)
10
20
(iv)
16.7778
(v)
6
Question
14
14.
Which of the following are true?
a)
18
11
−
(
108
17
✕
1
19
)
=
(
18
11
−
108
17
)
✕
(
18
11
−
1
19
)
b)
10
7
✕
(
59
17
+
7
5
)
=
(
10
7
✕
59
17
)
+
(
10
7
✕
7
5
)
c)
18
11
÷
(
59
17
+
1
4
)
=
(
18
11
÷
59
17
)
+
(
18
11
÷
1
4
)
d)
10
7
✕
(
108
17
−
19
13
)
=
(
10
7
✕
108
17
)
−
(
10
7
✕
19
13
)
(i)
{a,b}
(ii)
{c,d}
(iii)
{a,c,b}
(iv)
{b,d}
(v)
{a,d,b}
Question
15
15.
Find the difference of the rational numbers at the points labelled with letters E and F
(i)
-1
(ii)
(
-3
2
)
(iii)
(
-1
2
)
(iv)
1
2
(v)
(
-1
4
)
Question
16
16.
Find the rational number at the point labelled with letter S
(i)
(
-43
5
)
(ii)
(
-39
5
)
(iii)
(
-41
3
)
(iv)
(
-41
5
)
(v)
(
-41
7
)
Question
17
17.
Find the difference of the rational numbers at the points labelled with letters J and K
(i)
(
-3
5
)
(ii)
(
-1
5
)
(iii)
-1
(iv)
(
-3
7
)
Question
18
18.
Find the difference between the values of numbers at point A and B
(i)
1
3
(ii)
1
5
(iii)
(
-1
3
)
(iv)
1
Question
19
19.
Find the sum of the rational numbers at the points labelled with letters D and E
(i)
(
-19
2
)
(ii)
(
-41
4
)
(iii)
(
-21
2
)
(iv)
(
-23
2
)
(v)
-11
Question
20
20.
Rationalise the denominator of
(
−
5
√
7
+
4
√
2
)
(
−
2
√
6
−
√
8
)
=
(i)
(
5
8
√
40
−
1
2
√
12
−
5
8
√
14
+
1
)
(ii)
(
5
8
√
42
−
1
2
4
√
12
−
5
8
√
14
+
1
)
(iii)
(
5
8
√
42
−
1
2
√
12
−
5
8
√
14
+
1
)
(iv)
(
5
8
√
42
−
1
2
√
12
−
5
8
4
√
14
+
1
)
(v)
(
5
8
√
42
−
1
2
√
12
−
5
8
√
14
+
3
)
Question
21
21.
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 division
d)
real numbers are closed under multiplication
(i)
{c,a,b}
(ii)
{c,b}
(iii)
{c,d}
(iv)
{c,a}
(v)
{a,b,d}
Question
22
22.
Find the product of the rational numbers at the points labelled with letters Q and R
(i)
128
7
(ii)
56
3
(iii)
94
5
(iv)
92
5
(v)
18
Question
23
23.
Find the product of the rational numbers at the points labelled with letters M and N
(i)
2254
25
(ii)
2258
25
(iii)
2256
25
(iv)
2076
23
(v)
812
9
Question
24
24.
Rationalise the denominator of
(
√
5
+
√
2
)
(
√
4
+
√
3
)
=
(i)
(
2
√
5
+
2
√
2
−
√
15
−
√
6
)
(ii)
(
2
√
2
+
2
√
2
−
√
15
−
√
6
)
(iii)
(
2
√
5
+
2
√
2
−
√
15
−
√
9
)
(iv)
(
2
√
5
+
2
4
√
2
−
√
15
−
√
6
)
(v)
(
2
√
5
+
2
√
2
−
4
√
15
−
√
6
)
Question
25
25.
Which of the following is a rational number?
(i)
3
√
42
(ii)
3
√
24
(iii)
√
82
(iv)
3
√
18
(v)
4
5
Assignment Key
1) (i)
2) (v)
3) (v)
4) (ii)
5) (iii)
6) (iii)
7) (iv)
8) (iii)
9) (iv)
10) (ii)
11) (ii)
12) (ii)
13) (ii)
14) (iv)
15) (iii)
16) (iv)
17) (i)
18) (i)
19) (iii)
20) (iii)
21) (v)
22) (iv)
23) (iii)
24) (i)
25) (v)
