Cubes and Cube Roots

Exercise 1

1.    Which of the following numbers are not perfect cubes:

(i) 216                            (ii) 128

(iii) 1000                      (iv) 100

(v) 46656

2.    Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i) 243                           (ii) 256

(iii) 72                           (iv) 675

(v) 100

3.    Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

(i) 81                              (ii) 128

(iii) 135                          (iv) 192

(v) 704

4.    Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?


Exercise 2

5.   Find the cube root of each of the following numbers by prime factorization method:

(ii) 64                 (ii) 512

(iii) 10648         (iv) 27000

(v) 15625           (vi) 13824

(viii) 110592     (viii) 46656

(ix) 175616        (x) 91125

6.    State true or false:

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeroes.

(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 two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

7.    You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768.