Question

6 Are the given numbers perfect cubes? Test
them using prime factorisation,
A. 400
C. 2,700
D. 10,648
E. 46,656​

Answer 1

Answer:

d and e are perfect cube and a is perfect square but c is not a square and not a perfect cube

see step by step solution to understand

Step-by-step explanation:

2/400

2)200

2/100

2/50

5/25

5/5

1

2*2*2*2*5*5 =500 so it is not a perfect cube but it is perfect square of 20

now

2/2,700

2/1350

5/675

5/135

3/27

3/9

3/3

1

2*2*5*5*3*3*3=2700

so it is not perfect cube

now

2/10648

2/5324

2/2662

11/1331

11/121

11/11

1

2*2*2*11*11*11=10648

so it is perfect cube of 11*2=22

now

2/46656

2/23328

2/11664

2/5832

2/2916

2)1458

9/729

9/81

9/9

1

2*2*2*2*2*2*9*9*9 =46656

so it is perfect cube of 2*2*9=36

therefore

d and e are perfect cube and a is perfect square but c is not a perfect square and not a perfect cube

hope you get your an answer

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