Question

1. Which of the following is correct?
I. Cube of a negative number is always positive.
II. Cube of a negative number is always negative.
III. Cube of a negative number may be positive or negative.
IV. All of the above

Answer 1

(A)is correct

A negative number's cube root will always be negative

Since cubing a number means raising it to the 3rd power—which is odd—the cube roots of negative numbers must also be negative. This applies to perfect cubes and estimating other cube roots.

Answer 2

Answer:

Which of the following is correct?

II. Cube of a negative number is always negative.

Step-by-step explanation:

In the rules of multiplication, it is well known that

i. Negative number when multiplied with positive number, the answer is always a negative number. ( -ve × +ve = -ve )

ii. Negative number when multiplied with negative number, the answer is always a positive number. ( -ve × -ve = +ve )

iii. Positive number when multiplied with positive number, the answer is always a positive number. ( +ve × +ve = +ve )

Cube of any number can be get by multiplying that number with the same number for three times. Such as if we have to find the cube of 3, we will multiply

3×3×3 = 27.

Now, consider we have to find the cube of a negative number i.e. -3

∴ (-3) × (-3) = 9 (∵ -ve × -ve = +ve )

again we have to multiply 9 by -3, we get

9 × (-3) = -27 (∵ -ve × +ve = -ve )

Hence, it is proved that cube of a negative number is always negative.