# Cubes and Cube roots

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### Mathematics:

Mathematics Cubes and Cube roots Click the buttons for moving

### Which of the following numbers are not perfect cubes? (i) 216 (ii)128 :

Which of the following numbers are not perfect cubes? (i) 216 (ii)128 2 216 2 108 2 54 3 27 3 9 3 3 1 216 = 2x2x2 x 3x3x3 = 2 3 x 3 3 = 6 3 It’s a perfect cube

### (ii) 128:

(ii) 128 2 128 2 64 2 32 2 16 2 8 2 4 2 128 = 2x2x2x2x2x2x2 = 2 3 x2 3 x2 It’s a not perfect cube

### Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube. (i) 243 (ii) 72 (iii) 256:

Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube. (i) 243 (ii) 72 (iii) 256 243 3 243 3 81 3 27 3 9 3 243 = 3x3x3x3x3 3 must be multiplied to obtain perfect cube.

### (ii) 72:

(ii) 72 2 72 2 36 2 18 3 9 3 72 = 2x2x2x3x3 3 must be multiplied to obtain a perfect cube.

### (iii) 256:

(iii) 256 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 256 = 2x2x2x2x2x2x2x2 2 must be multiplied to obtain a perfect cube.

### Find the smallest number by which each of the following must be divided to obtain a perfect cube. (i) 81 (ii) 128:

Find the smallest number by which each of the following must be divided to obtain a perfect cube. (i) 81 (ii) 128 3 81 3 27 3 9 3 81= 3x3x3x3 3 must be divided to obtain a perfect cube .

### (ii) 128:

(ii) 128 2 128 2 64 2 32 2 16 2 8 2 4 2 128= 2x2x2x2x2x2x2 2 must be divided to obtain a perfect cube.

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

Parikshit makes a cuboid of plasticine of sides 5cm, 2cm, 5cm. How many such cuboid will he need to form a cube. 5 x 2 x 5cm If we multiply 5x2 2 will easier. Therefore, No. of cuboids needed = 5x2 2 = 5x4 or 20 Therefore, It needs 20 cuboids to make it cube.

### Find the cube root of each of the following numbers by prime factorisation.(i) 64 (ii) 10648 (iii) 27000:

Find the cube root of each of the following numbers by prime factorisation.(i) 64 (ii) 10648 (iii) 27000 2 64 2 32 2 16 2 8 2 4 2 3 64= 3 2x2x2x2x2x2 = 3 2 3 x2 3 = 2x2 = 4

### (ii)10648:

(ii)10648 2 10648 2 5324 2 2662 11 1331 11 121 11 11 1 3 10648 = 3 2x2x2x11x11x11 = 2x11 =22

### (iii)27000:

(iii)27000 2 27000 2 13500 2 6750 3 3375 3 1125 3 375 5 125 5 25 5 5 1 = 2x2x2x3x3x3x5x5x5 =2x3x5 =30

### True or false:

True or false 1. Cube of any odd number is even. False 2. A perfect cube does not ends with two zeros. True 3. If square of a number ends with 5, then its cube ends with 25. False 4. There is no perfect cube which ends with 8. False 5. The cube of a two digit number may be a three digit number. False 6. The cube of a two digit number may have seven or more digits. False