Cubes and Cube Roots
1. Which of the following numbers are not perfect cubes:
(i) 216 (ii) 128
(iii) 1000 (iv) 100
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
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
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?
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.