Solution of Chapter 7. Cubes and Cube Roots (NCERT - Mathematics Book)

Which of the following numbers are not perfect cubes?

(i) 216 (ii) 128

(iii) 1000 (iv) 100

(v) 46656

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

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

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?

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

(i) 64 (ii) 512

(iii) 10648 (iv) 27000

(v) 15625 (vi) 13824

(vii) 110592 (viii)46656

(ix) 175616 (x) 91125

State true or false

(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 two digit number may have seven or more digits

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

You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768