Question

8. Which of the following numbers is not a perfect cube? A) (-1)*2*2*3*3*3*4*4 B) 2*2*4*4*8*8 с 5*15*45 D All are perfect cube​

Answer 1

Answer:

Step-by-step explanation:

d) All are perfect cubes

Answer 2

Perfect cube

Step-by-step explanation:

Perfect cube is any integer that is equal to another integer raise to the power three.

For Example:

2³ = 2 × 2 × 2 = 4 × 2 = 8, therefore 8 is a perfect cube that is equal to 2 raise to the power 3.

Now we will check the given options:

A. (-1) × 2 × 2 × 3 × 3 × 3 × 4 × 4

• = ( -1 ) × 2 × 2 × 3 × 3 × 3 × ( 2 × 2 ) × ( 2 × 2 )
• = ( -1 ) × ( 2 × 2 × 2 ) × ( 2 × 2 × 2 ) × ( 3 × 3 × 3 )
• = -1³  ×  2³  × 2³  ×  3³
• Therefore, A is a perfect square.

B. 2 × 2 × 4 × 4 × 8 × 8

• = 2 × 2 × ( 2 × 2 ) × ( 2 × 2 ) × ( 2 × 2 × 2 ) × ( 2 × 2 × 2 )
• = ( 2 × 2 × 2 ) × ( 2 × 2 × 2 ) × ( 2 × 2 × 2 ) × ( 2 × 2 × 2 )
• = 2³  ×  2³  ×  2³  ×  2³
• Therefore B, is also a perfect square.

C. 5 × 15 × 45

• = 5 × 3 × 5 × 3 × 3 × 5
• = ( 3 × 3 × 3 ) × ( 5 × 5 × 5 )
• = 3³ × 5³
• Therefore, C is also a perfect square.

Hence the option D i.e., all are perfect cube is correct.