EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Find the difference between the values of numbers at point A and B
(i)
1
8
(ii)
1
6
(iii)
1
10
(iv)
3
8
(v)
(
-1
8
)
Question
2
2.
Rationalise the denominator of
1
9
√
8
(i)
1
18
(ii)
1
36
√
5
(iii)
1
36
4
√
2
(iv)
1
36
√
-1
(v)
1
36
√
2
Question
3
3.
Rationalise the denominator of
1
(
√
6
+
√
9
)
(i)
(
−
1
3
√
6
+
0
)
(ii)
(
−
1
3
√
8
+
1
)
(iii)
(
−
1
3
√
6
+
1
)
(iv)
(
−
1
3
√
3
+
1
)
(v)
(
−
1
3
√
6
+
2
)
Question
4
4.
Rationalise the denominator of
1
(
−
5
√
8
+
2
√
6
)
(i)
(
−
5
88
√
2
−
3
44
)
(ii)
(
−
5
88
√
2
−
1
88
4
√
6
)
(iii)
(
−
5
88
√
4
−
1
88
√
6
)
(iv)
(
−
5
88
√
-1
−
1
88
√
6
)
(v)
(
−
5
88
√
2
−
1
88
√
6
)
Question
5
5.
Find the difference of the rational numbers at the points labelled with letters H and I
(i)
(
-1
2
)
(ii)
(
-7
10
)
(iii)
(
-7
12
)
(iv)
(
-7
8
)
(v)
(
-9
10
)
Question
6
6.
Find the position of the rational number
9
2
on the number line
(i)
I
(ii)
S
(iii)
F
(iv)
Q
(v)
K
Question
7
7.
Which of the following are true?
a)
14
11
+
17
2
=
17
2
+
14
11
b)
3
5
÷
32
3
=
32
3
÷
3
5
c)
14
11
✕
32
3
=
32
3
✕
14
11
d)
3
5
−
17
2
=
17
2
−
3
5
(i)
{b,a}
(ii)
{a,c}
(iii)
{d,c}
(iv)
{b,c,a}
(v)
{b,d,a}
Question
8
8.
The rationalising factor of
(
−
3
√
4
−
7
√
3
)
=
(i)
(
−
6
+
7
√
3
)
(ii)
(
−
6
+
21
)
(iii)
(
−
6
+
7
4
√
3
)
(iv)
(
−
9
+
7
√
3
)
(v)
(
−
3
+
7
√
3
)
Question
9
9.
Find the sum of the rational numbers at the points labelled with letters K and L
(i)
(
-109
10
)
(ii)
(
-21
2
)
(iii)
(
-127
12
)
(iv)
(
-107
10
)
(v)
(
-87
8
)
Question
10
10.
Which of the following are true?
a)
3
16
÷
(
43
10
÷
1
15
)
=
(
3
16
÷
43
10
)
÷
1
15
b)
19
14
✕
(
43
10
✕
1
8
)
=
(
19
14
✕
43
10
)
✕
1
8
c)
19
14
+
(
52
17
+
7
10
)
=
(
19
14
+
52
17
)
+
7
10
d)
3
16
−
(
52
17
−
4
13
)
=
(
3
16
−
52
17
)
−
4
13
(i)
{d,c}
(ii)
{a,c,b}
(iii)
{b,c}
(iv)
{a,d,b}
(v)
{a,b}
Question
11
11.
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 multiplication
d)
real numbers are closed under division
(i)
{d,a,b}
(ii)
{d,a}
(iii)
{d,c}
(iv)
{d,b}
(v)
{a,b,c}
Question
12
12.
Rationalise the denominator of
(
√
6
+
√
3
)
(
−
√
6
+
√
5
)
=
(i)
(
−
6
−
4
√
18
−
√
30
−
√
15
)
(ii)
(
−
8
−
√
18
−
√
30
−
√
15
)
(iii)
(
−
6
−
√
18
−
4
√
30
−
√
15
)
(iv)
(
−
6
−
√
18
−
√
30
−
√
18
)
(v)
(
−
6
−
√
18
−
√
30
−
√
15
)
Question
13
13.
Find the difference of the rational numbers at the points labelled with letters H and I
(i)
(
-3
5
)
(ii)
(
-1
3
)
(iii)
1
5
(iv)
(
-1
5
)
(v)
(
-1
7
)
Question
14
14.
Find the rational number at the point labelled with letter I
(i)
45
8
(ii)
47
6
(iii)
47
10
(iv)
47
8
(v)
49
8
Question
15
15.
Find the product of the rational numbers at the points labelled with letters N and O
(i)
451
25
(ii)
453
25
(iii)
487
27
(iv)
415
23
(v)
449
25
Question
16
16.
Which of the following are true?
a)
rational numbers are closed under addition
b)
rational numbers are closed under subtraction
c)
rational numbers are closed under division
d)
rational numbers are closed under multiplication
(i)
{c,d}
(ii)
{c,a}
(iii)
{c,a,b}
(iv)
{c,b}
(v)
{a,b,d}
Question
17
17.
Rationalise the denominator of
(
8
√
2
−
3
√
3
)
(
−
2
√
6
−
5
√
2
)
=
(i)
(
8
13
√
12
−
3
13
√
18
−
46
15
+
15
26
√
6
)
(ii)
(
8
13
√
10
−
3
13
√
18
−
40
13
+
15
26
√
6
)
(iii)
(
8
13
√
12
−
3
13
√
18
−
40
13
+
15
26
√
8
)
(iv)
(
8
13
√
12
−
3
13
4
√
18
−
40
13
+
15
26
√
6
)
(v)
(
8
13
√
12
−
3
13
√
18
−
40
13
+
15
26
√
6
)
Question
18
18.
Find the rational number at the point labelled with letter M
(i)
(
-9
2
)
(ii)
(
-31
6
)
(iii)
(
-29
6
)
(iv)
(
-29
4
)
(v)
(
-29
8
)
Question
19
19.
The rationalising factor of
(
−
5
√
88
)
=
(i)
√
22
(ii)
√
25
(iii)
22
(iv)
√
20
(v)
4
√
22
Question
20
20.
Which of the following are true?
a)
7
16
−
(
27
10
✕
1
16
)
=
(
7
16
−
27
10
)
✕
(
7
16
−
1
16
)
b)
7
16
÷
(
35
4
+
1
8
)
=
(
7
16
÷
35
4
)
+
(
7
16
÷
1
8
)
c)
3
5
✕
(
27
10
−
2
15
)
=
(
3
5
✕
27
10
)
−
(
3
5
✕
2
15
)
d)
3
5
✕
(
35
4
+
16
17
)
=
(
3
5
✕
35
4
)
+
(
3
5
✕
16
17
)
(i)
{b,d}
(ii)
{a,c}
(iii)
{a,d,c}
(iv)
{a,b,c}
(v)
{c,d}
Question
21
21.
Find the sum of the rational numbers at the points labelled with letters S and T
(i)
16
(ii)
18
(iii)
12
(iv)
15
(v)
14
Question
22
22.
Find the product of the rational numbers at the points labelled with letters R and S
(i)
2257
98
(ii)
461
20
(iii)
2303
100
(iv)
2301
100
(v)
783
34
Question
23
23.
Find the position of the rational number
(
-20
3
)
on the number line
(i)
P
(ii)
J
(iii)
G
(iv)
S
(v)
F
Question
24
24.
Which of the following is a rational number?
(i)
3
√
98
(ii)
√
56
(iii)
2
15
(iv)
√
72
(v)
3
√
68
Question
25
25.
Which of the following is an irrational number?
(i)
10
23
(ii)
3
√
31
(iii)
21
(iv)
0.3333
(v)
3
Assignment Key
1) (i)
2) (v)
3) (iii)
4) (v)
5) (ii)
6) (v)
7) (ii)
8) (i)
9) (iv)
10) (iii)
11) (v)
12) (v)
13) (iv)
14) (iv)
15) (i)
16) (v)
17) (v)
18) (iii)
19) (i)
20) (v)
21) (iv)
22) (iii)
23) (ii)
24) (iii)
25) (ii)
