ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Cube of an even natural number is …………..
(ii) Cubes of natural numbers are called …………..
(iii) Cube of a natural number whose unit digit is 7, ends with digit …………..
(iv) If a natural number has one zero at its end, then its cube will contain ………….. zero at the end.
(v) Finding a cube root is the inverse operation of finding …………..
(vi) If a number can be expressed as the triplets of equal prime factors, then it is called …………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeros.
(iii) If square of a number ends with 5, then its cube ends with 25.
(iv) There is no perfect cube which ends with 8.
(v) The cube of a two digit number may be a three digit number.
(vi) The cube of a single digit number may be asingle digit number.
(vii) If a number is multiplied by 2 then its cube is multiplied by 8.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 12):
Question 3.
Cube of a negative number is
(a) negative
(b) positive
(c) negative or positive
(d) None of these.
Solution:

Question 4.
The unit digit of a cube of 476 is
(a) 4
(b) 6
(c) 8
(d) 2
Solution:

Question 5.
Cube of (-8) is
(a) -512
(b) 512
(c) -64
(d) 64
Solution:

Question 6.
Cube of \(\left(\frac{-3}{7}\right)\) is

Solution:

Question 7.
Cube root of -1331 is
(a) 11
(b) 21
(c) -11
(d) -21
Solution:

Question 8.
Cube root of 2744 is
(a) 16
(b) 18
(c) -14
(d) 14
Solution:

Question 9.
Cube root of \(1 \frac{127}{216}\) is

Solution:

Question 10.
The smallest number by which 192 should be multiplied to make it a perfect cube is
(a) 9
(b) 6
(c) 3
(d) 2
Solution:

Question 11.
The smallest number by which 686 should be divided to make it a perfect cube is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 12.
The volume of a cube is 729 m³. Length of its side is
(a) 3 m
(b) 6 m
(c) 9 m
(d) 27 m
Solution:

Value Based Question
Question 1.
A school decided to award prizes to their students for three values honesty, punctuality and obedience. If the number of students getting prizes for honesty, punctuality and obedience are in the ratio 1 : 2 : 3 and their product is 162, find the number of students getting prizes for each value.
Which quality you prefer to be rewarded most and why? What values are being promoted?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Find the volume of a cubical box if the cost of painting its outer surface is ₹1440 at the rate of ₹15 per sq. m.
Solution:

Question 2.
In a Maths lab there are some cubes and cuboids of the following measurements:
(i) one cube of side 4 cm
(ii) one cube of side 6 cm
(iii) 3 cuboids each of dimensions 4 cm × 4 cm × 6 cm and 3 cuboids each of the dimensions 4 cm × 6 cm × 6 cm.
A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find the length of side of new cube so formed.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2

Question 1.
Find the cube root of each of the following numbers by prime factorisation:
(i) 12167
(ii) 35937
(iii) 42875
(iv) 21952
(v) 373248
(vi) 32768
(vii) 262144
(viii) 157464
Solution:

Question 2.
Find the cube root of each of the following cube numbers through estimation.
(i) 19683
(ii) 59319
(iii) 85184
(iv) 148877
Solution:

Question 3.
Find the cube root of each of the following numbers:

Solution:

Question 4.
Evaluate the following:
(i) \(\sqrt[3]{512 \times 729}\)
(ii) \(\sqrt[3]{(-1331) \times(3375)}\)
Solution:

Question 5.
Find the cube root of the following decimal numbers:
(i) 0.003375
(ii) 19.683
Solution:

Question 6.
Evaluate: \(\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}\)
Solution:

Question 7.
Multiply 6561 by the smallest number so that product is a perfect cube. Also find the cube root of the product.
Solution:

Question 8.
Divide the number 8748 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient.
Solution:

Question 9.
The volume of a cubical box is 21952 m³. Find the length of the side of the box.
Solution:

Question 10.
Three numbers are in the ratio 3 : 4 : 5. If their product is 480, find the numbers.
Solution:

Question 11.
Two numbers are in the ratio 4 : 5. If the difference of their cubes is 61, find the numbers.
Solution:

Question 12.
The difference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1

Question 1.
Which of the following numbers are not perfect cubes? Give reasons in support of your answer:
(i) 648
(ii) 729
(iii) 8640
(iv) 8000
Solution:

Question 2.
Show that each of the following numbers is a perfect cube. Also, find the number whose cube is the given number:
(i) 1728
(ii) 5832
(iii) 13824
(iv) 35937
Solution:

Question 3.
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
(i) 243
(ii) 3072
(iii) 11979
(iv) 19652
Solution:

Question 4.
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
(i) 1536
(ii) 10985
(iii) 28672
(iv) 13718
Solution:

Question 5.
Rahul makes a cuboid of plasticine of sides 3 cm × 3 cm × 5 cm. How many such cuboids will he need to form a cube?
Solution:

Question 6.
Find the volume of a cubical box whose surface area is 486 cm².
Solution:

Question 7.
Which of the following are cubes of even natural numbers or odd natural numbers:
(i) 125
(ii) 512
(iii) 1000
(iv) 2197
(v) 4096
(vi) 6859
Solution:

Question 8.
Write the ones digit of the cube of each of the following numbers:
(i) 231
(ii) 358
(iii) 419
(iv) 725
(v) 854
(vi) 987
(vii) 752
(viii) 893
Solution:

Question 9.
Find the cubes of the following numbers:
(i) 13
(ii) \(3 \frac{1}{5}\)
(iii) \(-5 \frac{1}{7}\)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress

Question 1.
Show that 1089 is a perfect square. Also, find the number whose square is 1089.
Solution:

Question 2.
Find the smallest number which should be multiplied by 3675 to make it a perfect square. Also, find the square root of this perfect square.
Solution:

Question 3.
Express 121 as the sum of 11 odd numbers.
Solution:

Question 4.
How many numbers lie between 99² and 100²?
Solution:

Question 5.
Write a Pythagorean triplet whose one number is 17.
Solution:

Question 6.
Find the smallest square number which is divisible by each of the numbers 6, 8, 9.
Solution:

Question 7.
In an auditorium, the number of rows is equal to a number of chairs in each row. If the capacity of the auditorium is 1764. Find the number of chairs in each row.
Solution:

Question 8.
Find the length of diagonal of a rectangle whose length and breadth are 12 m and 5 m respectively.
Solution:

Question 9.
Find the square root of 144 by successive subtraction.
Solution:

Question 10.
Find the square root of the following numbers by prime factorisation:
(i) 5625
(ii) 1521
Solution:

Question 11.
Find the square root of the following numbers by long division method:
(i) 21904
(ii) 108241
Solution:

Question 12.
Find the square root of following decimal numbers:
(i) 17.64
(ii) 13.3225
Solution:

Question 13.
Find the square root of the following fractions:

Solution:

Question 14.
Find the least number which must be subtracted from 2311 to make it a perfect square.
Solution:

Question 15.
Find the least number which must be added to 520 to make it a perfect square.
Solution:

Question 16.
Find the greatest number of 5 digits which is a perfect square.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A number ending in ……… is never a perfect square.
(ii) On combining two consecutive triangular number, we get a ………
(iii) If a number has digits ……… in the unit’s place, then its square ends in 1.
(iv) Sum of the first 10 odd natural numbers is ………
(v) A number of non-square numbers between 11² and 12² is ………
(vi) Number of zeros in the end of the square of 400 is ………
(vii) Square of any ……… number can be expressed as the sum of two consecutive natural numbers.
(viii)For a natural number m > 1, (2m, m² – 1, m² + 1) is called ………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) All-natural numbers are not perfect squares.
(ii) A perfect square can never be expressed as the product of pairs of equal prime factors.
(iii) A number having 2,3,7 or 8 at its unit place is never a square number.
(iv) A number having 0, 1, 4, 5, 6 or 9 at its unit place is always a square number.
(v) A number ending in an even number of zeros is always a perfect square.
(vi) Square of an odd number is always an odd number.
(vii) 1, 3, 6, 10, 15, are called triangular numbers.
(viii)There are 2n non-square numbers between the squares of consecutive numbers n and (n + 1).
(ix) (4, 6, 8) is a Pythagorean triplet.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 15):
Question 3.
How many natural numbers lie between 25² and 26²?
(a) 49
(b) 50
(c) 51
(d) 52
Solution:

Question 4.
Square of an even number is always
(a) even
(b) odd
(c) even or odd
(d) none of these
Solution:

Question 5.
1+ 3 + 5 + 7 + ……….. up to n terms is equal to
(a) n² – 1
(b) (n + 1)²
(c) n² + 1
(d) n²
Solution:

Question 6.
\(\sqrt{208+\sqrt{2304}}\) is equal to
(a) 18
(b) 16
(c) 14
(d) 22
Solution:

Question 7.
\(\sqrt{0.0016}\) is equal to
(a) 0.04
(b) 0.004
(c) 0.4
(d) none of these
Solution:

Question 8.
The smallest number by which 75 should be divided to make it a perfect square is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 9.
\(\sqrt{3 \frac{6}{25}}\) is equal to

Solution:

Question 10.
The smallest number by which 162 should be multiplied to make it a perfect square is
(a) 4
(b) 3
(c) 2
(d) 1
Solution:

Question 11.
If the area of a square field is 961 unit², then the length of its side is
(a) 29 units
(b) 41 units
(c) 31 untis
(d) 39 units
Solution:

Question 12.
The smallest number that should be subtracted from 300 to make it a perfect square is
(a) 11
(b) 12
(c) 13
(d) 14
Solution:

Question 13.
If one number of the Pythagorean triplet is 6, then the triplet is
(a) (4, 5, 6)
(b) (5, 6, 7)
(c) (6, 7, 8)
(d) (6, 8, 10)
Solution:

Question 14.
nth triangular number is

Solution:

Question 15.
Given that \(\sqrt{1521}\) = 39, the value of \(\sqrt{0.1521}+\sqrt{15.21}\) is
(a) 42.9
(b) 4.29
(c) 3.51
(d) 35.1
Solution:

Value Based Questions
Question 1.
In a school, students of class VIII collected ₹9216 to give a donation to an NGO working for the education of poor children. If each student donated as many rupees as the number of students in class VIII. Find the number of students in class VIII.
Why should we donate money for the education of poor children? What values are being promoted?
Solution:

Question 2.
A person wants to plant 2704 medicinal plants with a board depicting the diseases in which that can be used. He planted these in the form of rows. If each row contains as many plants as the number of rows, then find the number of rows.
Why should we plant medicinal plants? What values are being promoted?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
A square field is to be ploughed. Ramu get it ploughed in ₹34560 at the rate of ₹15 per sq. m. Find the length of side of square field.
Solution:

Question 2.
Lalit has some chocolates. He distributed these chocolates among 13 children in such a way that he gave one chocolate to first child, 3 chocolates to the second child, 5 chocolates to third and so on. Find the number of chocolates Lalit had.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths