Question

5.1 State whether the following statements are always true. If not, explain why
(a) The cubes of 18, 20, and 26 are all odd numbers.
(b) The cubes of 12, 22, and 28 will all end in 8.​

Answer 1

Answer:

(a) false

(b) false

Step-by-step explanation:

(a)

=> 18³ = 5832 (even)

=> 20³ = 8000 (even)

=> 26³ = 17576 (even)

∴The statement is false.

(b)

12³ = 1728

22³ = 10648

28³ = 21952 ( ends in 2)

∴The statement is false.

Answer 2

Answer:

(a) false

(b) false

Step-by-step explanation:

(a) The cubes of $18, 20 \ and \ 26$ are:

$18^{3} = 5832$

$20^{3} = 8000$

$26^{3} = 17576$

⇒ $5832, 8000, 17576$ are all even numbers, hence the given statement is false.

(b) The cubes of $12, 22, \ and \ 28$ are:

$12^{3} = 1728\\22^{3} = 10648\\28^{3} = 21952$

⇒ Only $1728 \ and \ 10648$ end in $8$. Hence, the given statement is false.

Final Answer:

The correct statements instead will be:

(a) The cubes of 18, 20, and 26 are all even numbers.

(b) The cubes of 12 and 22 end in 8. The cube of 28 ends in 2.​

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