EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Real Numbers
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Rationalise the denominator of
1
(
−
√
6
−
√
9
)
(i)
(
1
3
√
6
−
2
)
(ii)
(
1
3
√
6
−
1
)
(iii)
(
1
3
√
9
−
1
)
(iv)
(
1
3
√
4
−
1
)
(v)
(
1
3
√
6
+
0
)
Question
2
2.
Which of the following are true?
a)
real numbers are closed under addition
b)
real numbers are closed under subtraction
c)
real numbers are closed under multiplication
d)
real numbers are closed under division
(i)
{d,c}
(ii)
{d,b}
(iii)
{a,b,c}
(iv)
{d,a,b}
(v)
{d,a}
Question
3
3.
The rationalising factor of
(
−
2
√
32
)
=
(i)
√
5
(ii)
2
(iii)
√
2
(iv)
4
√
2
(v)
√
-1
Question
4
4.
Find the product of the rational numbers at the points labelled with letters G and H
(i)
1894
25
(ii)
378
5
(iii)
1742
23
(iv)
1892
25
(v)
2042
27
Question
5
5.
Rationalise the denominator of
(
5
√
5
+
2
√
9
)
(
√
2
+
3
√
3
)
=
(i)
(
−
1
5
√
7
−
6
25
√
2
+
3
5
√
15
+
18
25
√
3
)
(ii)
(
−
1
5
√
10
−
6
25
√
2
+
3
5
√
15
+
18
25
√
3
)
(iii)
(
−
1
5
√
10
−
6
25
4
√
2
+
3
5
√
15
+
18
25
√
3
)
(iv)
(
−
1
5
√
10
−
6
25
√
2
+
3
5
4
√
15
+
18
25
√
3
)
(v)
(
−
1
5
√
10
−
6
25
√
2
+
3
5
√
15
+
18
25
√
5
)
Question
6
6.
Find the position of the rational number
(
-37
9
)
on the number line
(i)
F
(ii)
E
(iii)
K
(iv)
I
(v)
L
Question
7
7.
Which of the following are true?
a)
16
13
−
(
104
19
−
6
17
)
=
(
16
13
−
104
19
)
−
6
17
b)
16
13
÷
(
19
11
÷
13
16
)
=
(
16
13
÷
19
11
)
÷
13
16
c)
7
6
✕
(
19
11
✕
6
5
)
=
(
7
6
✕
19
11
)
✕
6
5
d)
7
6
+
(
104
19
+
2
19
)
=
(
7
6
+
104
19
)
+
2
19
(i)
{a,d,c}
(ii)
{b,d}
(iii)
{c,d}
(iv)
{a,c}
(v)
{a,b,c}
Question
8
8.
Which of the following is a rational number?
(i)
√
45
(ii)
3
√
45
(iii)
√
74
(iv)
3
√
59
(v)
5
7
Question
9
9.
Which of the following is an irrational number?
(i)
√
98
(ii)
27
(iii)
(-2)
(iv)
9.8148
(v)
1
4
Question
10
10.
Find the difference of the rational numbers at the points labelled with letters E and F
(i)
(
-3
5
)
(ii)
(
-1
5
)
(iii)
-1
(iv)
(
-3
7
)
Question
11
11.
Rationalise the denominator of
1
5
√
3
(i)
1
15
√
6
(ii)
1
15
4
√
3
(iii)
1
5
(iv)
1
15
√
3
(v)
1
15
√
1
3
Question
12
12.
Rationalise the denominator of
(
−
√
5
+
√
4
)
(
−
√
9
+
√
7
)
=
(i)
(
3
2
√
5
−
3
+
1
2
√
35
−
√
10
)
(ii)
(
3
2
√
5
−
2
+
1
2
√
35
−
√
7
)
(iii)
(
3
2
√
5
−
3
+
1
2
4
√
35
−
√
7
)
(iv)
(
3
2
√
2
−
3
+
1
2
√
35
−
√
7
)
(v)
(
3
2
√
5
−
3
+
1
2
√
35
−
√
7
)
Question
13
13.
Find the sum of the rational numbers at the points labelled with letters K and L
(i)
(
-49
4
)
(ii)
(
-25
2
)
(iii)
(
-23
2
)
(iv)
-13
(v)
(
-27
2
)
Question
14
14.
Find the sum of the rational numbers at the points labelled with letters F and G
(i)
36
5
(ii)
38
5
(iii)
50
7
(iv)
22
3
(v)
34
5
Question
15
15.
Find the difference between the values of numbers at point A and B
(i)
(
-1
8
)
(ii)
(
-1
2
)
(iii)
(
-5
8
)
(iv)
(
-3
8
)
(v)
(
-3
10
)
Question
16
16.
Find the difference of the rational numbers at the points labelled with letters K and L
(i)
(
-1
5
)
(ii)
(
-3
5
)
(iii)
-1
(iv)
(
-3
7
)
Question
17
17.
Which of the following are true?
a)
19
13
÷
79
20
=
79
20
÷
19
13
b)
3
7
+
56
17
=
56
17
+
3
7
c)
19
13
−
56
17
=
56
17
−
19
13
d)
3
7
✕
79
20
=
79
20
✕
3
7
(i)
{b,d}
(ii)
{c,d}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{a,c,b}
Question
18
18.
Find the product of the rational numbers at the points labelled with letters E and F
(i)
1438
27
(ii)
1332
25
(iii)
266
5
(iv)
1334
25
(v)
1226
23
Question
19
19.
Which of the following are true?
a)
rational numbers are closed under multiplication
b)
rational numbers are closed under subtraction
c)
rational numbers are closed under addition
d)
rational numbers are closed under division
(i)
{a,b,c}
(ii)
{d,b}
(iii)
{d,a}
(iv)
{d,c}
(v)
{d,a,b}
Question
20
20.
Find the rational number at the point labelled with letter S
(i)
(
-28
5
)
(ii)
(
-26
5
)
(iii)
(
-28
3
)
(iv)
-6
(v)
-4
Question
21
21.
Find the position of the rational number
18
5
on the number line
(i)
J
(ii)
M
(iii)
D
(iv)
F
(v)
N
Question
22
22.
Find the rational number at the point labelled with letter M
(i)
13
2
(ii)
39
8
(iii)
41
8
(iv)
39
10
(v)
37
8
Question
23
23.
The rationalising factor of
(
−
√
9
+
7
√
5
)
=
(i)
(
−
6
−
7
√
5
)
(ii)
(
−
3
−
7
4
√
5
)
(iii)
(
−
3
−
35
)
(iv)
(
−
3
−
7
√
5
)
(v)
(
−
1
−
7
√
5
)
Question
24
24.
Rationalise the denominator of
1
(
−
4
√
5
+
8
√
7
)
(i)
(
1
92
√
5
+
1
46
4
√
7
)
(ii)
(
1
92
√
5
+
7
46
)
(iii)
(
1
92
√
2
+
1
46
√
7
)
(iv)
(
1
92
√
5
+
1
46
√
7
)
(v)
(
1
92
√
8
+
1
46
√
7
)
Question
25
25.
Which of the following are true?
a)
10
7
✕
(
22
3
+
7
2
)
=
(
10
7
✕
22
3
)
+
(
10
7
✕
7
2
)
b)
9
8
÷
(
22
3
+
9
17
)
=
(
9
8
÷
22
3
)
+
(
9
8
÷
9
17
)
c)
10
7
✕
(
24
13
−
20
7
)
=
(
10
7
✕
24
13
)
−
(
10
7
✕
20
7
)
d)
9
8
−
(
24
13
✕
9
2
)
=
(
9
8
−
24
13
)
✕
(
9
8
−
9
2
)
(i)
{b,c,a}
(ii)
{a,c}
(iii)
{d,c}
(iv)
{b,a}
(v)
{b,d,a}
Assignment Key
1) (ii)
2) (iii)
3) (iii)
4) (iv)
5) (ii)
6) (iii)
7) (iii)
8) (v)
9) (i)
10) (i)
11) (iv)
12) (v)
13) (ii)
14) (i)
15) (iv)
16) (ii)
17) (i)
18) (ii)
19) (i)
20) (i)
21) (iv)
22) (ii)
23) (iv)
24) (iv)
25) (ii)
