Download 1 - Mayor World School

Grade VIII
Mathematics Holiday Homework
"Life is like riding a bicycle. To keep your balance you must keep moving."
Albert
Einstein
General Instructions:
 Submit your work in a seperate thin notebook
 Present your work neatly
 Work out the rough calculations if required on the right side of the
notebook.
Assignment
Q1. Check whether the given numbers are perfect square or not. It not, then find the
smallest number by which the given number must be multiplied so as to get a perfect
square in each case. Also, find the square root of the new number formed.
(a) 6728
(b) 1452
(c) 2925
Ans. a) 2, 116
b) 3, 66
c) 13, 195
Q2. Check whether the given numbers are perfect squares or not. It not, then find the
smallest number by which the given number must be divided so as to get a perfect
square in each case. Also, find the square root of the number obtained.
(a) 624
(b) 396
(c) 2925
Ans. a) 39, 4
b) 11, 6
c) 13, 15
Q3. Find the square root of each of the following numbers by using the method of
prime factorization :
(a) 1681
(b) 6400
(d) 15876
(d) 562500
Ans. a) 41
b) 80
c) 126
d) 750
Q4. A welfare association collected Rs. 52900 as donation from the students. If each
paid as many rupees as there were students, find the number of students.
Ans. 230 students
Q5. Find the square root of each of the following by division method.
(a) 12544
(b) 17956
(c) 92416
(d) 22500
(e) 10404
Ans. a) 112
b) 134
c) 304
d) 150
e) 102
Q6. Find the smallest number which must be subtracted from the given numbers to
make them a perfect square.
(a) 36820
(b) 4931
Ans. a) 339
b) 31
Q7. Find the smallest number which must be added to the following numbers so as to
make them perfect square.
(a) 16160
(b) 7250
Ans. a) 224
b) 146
Q8. Find the smallest number by which the following must be multiplied to make
them the perfect cube.
(a) 3136
(b) 2560
(c) 14400
(d) 5400
Ans. a) 7
b) 25
c) 15
d) 5
Q9. Find the smallest number by which the following must be divided to make them
the perfect cube.
(a) 1323
(b) 1600
Ans. a) 49
b) 25
c) 2
(c) 1024
(d) 5324
d) 4
Q10. Find the cube roots of the following rational numbers :
10648
216
 343
(a)
(b)
(c)
12167
729
512
 2744
 2744
(d)
(e)
3375
1728
Ans. a)
6
9
b)
7
8
c)
22
23
d)
 14
15
e)
 14
12
Q11. Evaluate :
(a) 3 64 + 3 0.027 + 3 0.008
(b) 3 0.3  0.3  0.3  11  11  11
Ans. a) 4.5
b) 3.3
Q12. Find the least Perfect square number which is exactly divisible by 8. 9 and 10.
Ans. 3600
Q13. Find a rational number between the following :
1
2
(a)
and
(b) 4 and 5
(c) 2 and 1
3
5
1
1
1
1
(d)
and
(d)
and
2
4
4
3
Ans. a)
5
15
b)
9
2
c)
3
2
d)
Q14. Find three rational number between :
2
3
1
1
(a)
and
(b) and
3
4
3
2
3
8
e)
7
24
(c) 3 and 4
Ans. a)
33 34 35
,
,
48 48 48
b)
9 10 11
,
,
24 24 24
c)
31 32 33
,
,
10 10 10
Q15. State, yes or no.
(a) Is the sum of any two rational numbers also a rational number ?
(b) Is addition of rational numbers associative ?
(c) Is addition of rational numbers commutative ?
(d) Is negative of a negative rational number of positive ?
(e) Is subtraction of rational numbers commutative ?
(f) Rational number 0 is its own additive inverse ?
(g) Rational number 0 is additive identity of rational numbers ?
(h) Is the product of 0 and a rational number, the rational number itself ?
Ans. a) Yes b) Yes c) Yes d) Yes e) No f) Yes g) Yes h) No
1
Q16. Is 0.3 the multiplicative inverse of 3 ? Why or why not ?
3
10
3
Ans. Yes, the multiplicative inverse of
=
= 0.3
3
10
Q17. State whether the following statements are True or False :
(a) The quotient of two rational numbers is always a rational number.
(b) We can divide 1 by 0 ?
(c) In case of division of rational numbers : Commutative and associative properties
are applicable.
Ans. a) True b) False
c) False
Q18. Represent the following numbers on the number line.
2
1
(a)
(b) 6
7
2
Q,19 A man covers a distance of 50m in 40 steps. How many steps will be required to
cover a distance of 315m. Name the two variables and also the variation between
them herein this question.
Ans. 252 steps
Q,20 On a particular day, 100 US dollars are worth Rs. 4833. On that day, how many
dollars could be bought for Rs. 10149.30? Also name the variable and the variation
between them
Ans. 210 US dollars
Q.21 Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in
6 hours. If both are opened at the same time while the tank is empty,how much time
will they take to fill up the tank completely?
Ans. 30hours.
Q.22 A car takes 2 hours to reach a destination by travelling at the speed of 60km/hr.
How long will it take when the car travels at the speed of 80km/hr? Also name the
variables and the variation between them.
Ans. 1
1
hours.
2