Question

Q7. Which of the following 2 points
numbers is not a perfect
cube? (ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਪੂਰਨ
ਘਣ ਨਹੀਂ ਹੈ?)
O 792
0 343
O 512
0 216​

Answer 1

Question :- Which of the following 2 points

numbers is not a perfect

cube? (ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਪੂਰਨ

ਘਣ ਨਹੀਂ ਹੈ?)

O 792

0 343

O 512

0 216

Solution :-

As we know that, in perfect cube we make pairs of 3 of their prime factors.

So Lets check them one by one.

1) Prime Factors of 792 :-

→ 792 = 2 * 2 * 2 * 3 * 3 * 11

As we can see , only Prime number 2 is in pair of three .

Therefore, 792 is not a perfect cube.

2) Prime Factors of 343 :-

→ 343 = 7 * 7 * 7

As we can see , Prime number 7 is in pair of three .

Therefore, 343 is a perfect cube. (cube of 7).

3) Prime Factors of 512 :-

→ 512 = (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2)

As we can see , Prime number 2 is in pair of three , three times .

Therefore, 512 is a perfect cube. (cube of 2 * 2 * 2 = 8).

4) Prime Factors of 216 :-

→ 216 = 2 * 2 * 2 * 3 * 3 * 3

As we can see , Prime number 2 and 3 both are in pair of three .

Therefore, 216 is also a perfect cube. (cube of 2 * 3 = 6).

Hence, Only Number which is not a perfect cube is 792.