All questions of Cubes and Cube Roots for Class 8 Exam

Explanation:

When a number is doubled, its new value becomes 2x, where x is the original value of the number.

To find the cube of a number, we multiply it by itself three times. So, the cube of the original number x is x^3.

Now, we can use this information to determine which statement is correct:

a) its cube is two times the cube of the given number
- This statement is incorrect because 2x^3 is not equal to two times x^3.

b) its cube is there times the cube of the given number
- This statement is also incorrect because 3x^3 is not equal to the cube of 2x.

c) its cube is six times the cube of the given number
- This statement is incorrect because 6x^3 is not equal to the cube of 2x.

d) its cube is eight times the cube of the given number.
- This statement is correct because (2x)^3 is equal to 8x^3.

Therefore, the correct statement is option 'D'.

The correct statement is option 'c': The cube of a negative number may be positive or negative.

Explanation:
- A cube of a number is obtained by multiplying the number three times.
- When we cube a positive number, the result is always positive.
- However, when we cube a negative number, the result can be either positive or negative, depending on the number itself.
- Let's consider a few examples:

Example 1: Cube of -2
- (-2) x (-2) x (-2) = -8
- Here, the cube of -2 is negative.

Example 2: Cube of -3
- (-3) x (-3) x (-3) = -27
- Again, the cube of -3 is negative.

Example 3: Cube of -1
- (-1) x (-1) x (-1) = -1
- In this case, the cube of -1 is also negative.

Example 4: Cube of -4
- (-4) x (-4) x (-4) = -64
- Once again, the cube of -4 is negative.

Conclusion:
- From the above examples, we can see that the cube of a negative number can be negative.
- Therefore, option 'c': The cube of a negative number may be positive or negative, is the correct statement.

If the digits in one number are rearranged to form another number, the two numbers are said to be permutations of each other.