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
(
2
√
8
+
√
7
)
(i)
(
4
25
√
2
−
7
25
)
(ii)
(
4
25
√
2
−
1
25
√
7
)
(iii)
(
4
25
√
4
−
1
25
√
7
)
(iv)
(
4
25
√
2
−
1
25
4
√
7
)
(v)
(
4
25
√
1
2
−
1
25
√
7
)
Question
2
2.
Rationalise the denominator of
1
(
−
√
3
+
√
8
)
(i)
(
1
5
√
3
+
2
5
4
√
2
)
(ii)
(
1
5
√
3
+
2
5
√
2
)
(iii)
(
1
5
√
3
+
4
5
)
(iv)
(
1
5
√
6
+
2
5
√
2
)
(v)
(
1
5
√
1
3
+
2
5
√
2
)
Question
3
3.
Find the sum of the rational numbers at the points labelled with letters F and G
(i)
13
3
(ii)
19
5
(iii)
17
5
(iv)
21
5
(v)
25
7
Question
4
4.
Rationalise the denominator of
(
−
√
5
−
√
3
)
(
−
√
7
+
√
8
)
=
(i)
(
−
√
35
−
√
21
−
2
√
10
−
2
√
6
)
(ii)
(
−
√
33
−
√
21
−
2
√
10
−
2
√
6
)
(iii)
(
−
√
35
−
4
√
21
−
2
√
10
−
2
√
6
)
(iv)
(
−
√
35
−
√
21
−
2
√
10
−
2
√
9
)
(v)
(
−
√
35
−
√
21
−
2
4
√
10
−
2
√
6
)
Question
5
5.
The rationalising factor of
(
−
8
√
5
+
√
4
)
=
(i)
(
−
8
√
5
−
3
)
(ii)
(
−
8
√
5
−
2
)
(iii)
(
−
8
√
2
−
2
)
(iv)
(
−
8
√
8
−
2
)
(v)
(
−
8
√
5
−
1
)
Question
6
6.
Which of the following are true?
a)
7
12
−
(
83
9
✕
17
10
)
=
(
7
12
−
83
9
)
✕
(
7
12
−
17
10
)
b)
8
13
✕
(
83
9
−
17
12
)
=
(
8
13
✕
83
9
)
−
(
8
13
✕
17
12
)
c)
8
13
✕
(
25
7
+
10
3
)
=
(
8
13
✕
25
7
)
+
(
8
13
✕
10
3
)
d)
7
12
÷
(
25
7
+
13
16
)
=
(
7
12
÷
25
7
)
+
(
7
12
÷
13
16
)
(i)
{a,b}
(ii)
{b,c}
(iii)
{d,c}
(iv)
{a,d,b}
(v)
{a,c,b}
Question
7
7.
Which of the following are true?
a)
real numbers are closed under subtraction
b)
real numbers are closed under division
c)
real numbers are closed under multiplication
d)
real numbers are closed under addition
(i)
{b,a}
(ii)
{b,a,c}
(iii)
{a,c,d}
(iv)
{b,d}
(v)
{b,c}
Question
8
8.
Find the difference of the rational numbers at the points labelled with letters D and E
(i)
(
-7
10
)
(ii)
(
-1
2
)
(iii)
(
-9
10
)
(iv)
(
-7
8
)
(v)
(
-7
12
)
Question
9
9.
The rationalising factor of
5
√
70
=
(i)
√
67
(ii)
√
70
(iii)
4
√
70
(iv)
70
(v)
√
72
Question
10
10.
Find the difference between the values of numbers at point A and B
(i)
(
-3
7
)
(ii)
(
-1
9
)
(iii)
1
7
(iv)
(
-1
5
)
(v)
(
-1
7
)
Question
11
11.
Rationalise the denominator of
(
3
√
7
−
4
√
5
)
(
2
√
6
+
√
8
)
=
(i)
(
3
8
√
42
−
1
2
√
30
−
3
8
√
14
+
1
2
√
10
)
(ii)
(
3
8
√
40
−
1
2
√
30
−
3
8
√
14
+
1
2
√
10
)
(iii)
(
3
8
√
42
−
1
2
4
√
30
−
3
8
√
14
+
1
2
√
10
)
(iv)
(
3
8
√
42
−
1
2
√
30
−
3
8
4
√
14
+
1
2
√
10
)
(v)
(
3
8
√
42
−
1
2
√
30
−
3
8
√
14
+
1
2
√
13
)
Question
12
12.
Find the rational number at the point labelled with letter D
(i)
5
3
(ii)
7
3
(iii)
1
(iv)
5
Question
13
13.
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)
{d,a,b}
(ii)
{a,b,c}
(iii)
{d,b}
(iv)
{d,a}
(v)
{d,c}
Question
14
14.
Which of the following is an irrational number?
(i)
2
(ii)
(-5)
(iii)
16
28
(iv)
3
√
28
(v)
0.3333
Question
15
15.
Find the product of the rational numbers at the points labelled with letters P and Q
(i)
26
(ii)
27
(iii)
30
(iv)
24
(v)
28
Question
16
16.
Find the position of the rational number
22
3
on the number line
(i)
Q
(ii)
N
(iii)
R
(iv)
E
(v)
M
Question
17
17.
Find the sum of the rational numbers at the points labelled with letters P and Q
(i)
(
-85
7
)
(ii)
(
-61
5
)
(iii)
(
-59
5
)
(iv)
(
-37
3
)
(v)
(
-63
5
)
Question
18
18.
Find the product of the rational numbers at the points labelled with letters M and N
(i)
1904
23
(ii)
414
5
(iii)
2068
25
(iv)
248
3
(v)
2066
25
Question
19
19.
Rationalise the denominator of
1
2
√
9
(i)
1
6
(ii)
1
4
(iii)
1
8
(iv)
1
2
(v)
(
−
1
6
)
Question
20
20.
Which of the following are true?
a)
19
12
+
23
2
=
23
2
+
19
12
b)
13
17
−
23
2
=
23
2
−
13
17
c)
13
17
÷
35
3
=
35
3
÷
13
17
d)
19
12
✕
35
3
=
35
3
✕
19
12
(i)
{c,d}
(ii)
{a,d}
(iii)
{b,c,a}
(iv)
{b,d,a}
(v)
{b,a}
Question
21
21.
Find the rational number at the point labelled with letter G
(i)
-4
(ii)
(
-38
9
)
(iii)
(
-38
7
)
(iv)
(
-38
11
)
(v)
(
-40
9
)
Question
22
22.
Find the difference of the rational numbers at the points labelled with letters K and L
(i)
(
-1
2
)
(ii)
(
-1
4
)
(iii)
1
2
(iv)
-1
(v)
(
-3
2
)
Question
23
23.
Which of the following are true?
a)
9
5
−
(
37
18
−
8
3
)
=
(
9
5
−
37
18
)
−
8
3
b)
1
8
+
(
37
18
+
18
19
)
=
(
1
8
+
37
18
)
+
18
19
c)
9
5
÷
(
33
5
÷
1
13
)
=
(
9
5
÷
33
5
)
÷
1
13
d)
1
8
✕
(
33
5
✕
9
13
)
=
(
1
8
✕
33
5
)
✕
9
13
(i)
{a,b}
(ii)
{c,d}
(iii)
{b,d}
(iv)
{a,d,b}
(v)
{a,c,b}
Question
24
24.
Which of the following is a rational number?
(i)
3
√
12
(ii)
4
7
(iii)
√
40
(iv)
√
72
(v)
3
√
11
Question
25
25.
Find the position of the rational number
(
-17
3
)
on the number line
(i)
L
(ii)
R
(iii)
F
(iv)
I
(v)
J
Assignment Key
1) (ii)
2) (ii)
3) (ii)
4) (i)
5) (ii)
6) (ii)
7) (iii)
8) (i)
9) (ii)
10) (v)
11) (i)
12) (i)
13) (ii)
14) (iv)
15) (ii)
16) (v)
17) (ii)
18) (iii)
19) (i)
20) (ii)
21) (ii)
22) (i)
23) (iii)
24) (ii)
25) (i)
