Answer

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Hint: A cube number is a number multiplied by itself \[3\]times. This can also be called a ‘a number cubed’. The cube root of a number is another number that, when you multiply it by itself three times, gives you the original number.

Consider the option A. \[ - 1,1\]

Here the cube of \[ - 1\] is \[ - 1 \times - 1 \times - 1 = - 1\] and cube root of \[ - 1\] is \[\sqrt[3]{{ - 1}} = - 1\]

And the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

Therefore, the numbers \[ - 1,1\] have the same cube and cube roots.

Consider option B. \[2, - 2\]

Here cube of \[2\] is \[2 \times 2 \times 2 = 8\] and cube root of \[2\] is \[\sqrt[3]{2} = 1.25992104989\]

And the cube of \[ - 2\] is \[ - 2 \times - 2 \times - 2 = - 8\] and cube root of \[ - 2\] is \[\sqrt[3]{{ - 2}} = - 1.2592104989\]

Therefore, the numbers \[2, - 2\] do not have the same cube and cube roots.

Consider the option C. \[1,2\]

Here the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

And the cube of \[2\] is \[2 \times 2 \times 2 = 8\] and cube root of \[2\] is \[\sqrt[3]{2} = 1.25992104989\]

Therefore, the numbers \[1,2\] do not have the same cube and cube roots.

Consider the option D. \[0,1\]

Here the cube of \[0\] is \[0 \times 0 \times 0 = 0\] and the cube root of \[0\]is \[\sqrt[3]{0} = 0\].

And the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

Therefore, the numbers \[0,1\] have the same cube and cube roots.

Thus, the correct options are A. \[ - 1,1\] and D. \[0,1\].

Note: In this problem you have to choose all the correct options. And it is not necessary to write the exact value of the cube root number, you can make them up to three decimal points. If one of the numbers in the option satisfies the conditions given in the problem and another number is not satisfied then that option is considered as an incorrect option.

Consider the option A. \[ - 1,1\]

Here the cube of \[ - 1\] is \[ - 1 \times - 1 \times - 1 = - 1\] and cube root of \[ - 1\] is \[\sqrt[3]{{ - 1}} = - 1\]

And the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

Therefore, the numbers \[ - 1,1\] have the same cube and cube roots.

Consider option B. \[2, - 2\]

Here cube of \[2\] is \[2 \times 2 \times 2 = 8\] and cube root of \[2\] is \[\sqrt[3]{2} = 1.25992104989\]

And the cube of \[ - 2\] is \[ - 2 \times - 2 \times - 2 = - 8\] and cube root of \[ - 2\] is \[\sqrt[3]{{ - 2}} = - 1.2592104989\]

Therefore, the numbers \[2, - 2\] do not have the same cube and cube roots.

Consider the option C. \[1,2\]

Here the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

And the cube of \[2\] is \[2 \times 2 \times 2 = 8\] and cube root of \[2\] is \[\sqrt[3]{2} = 1.25992104989\]

Therefore, the numbers \[1,2\] do not have the same cube and cube roots.

Consider the option D. \[0,1\]

Here the cube of \[0\] is \[0 \times 0 \times 0 = 0\] and the cube root of \[0\]is \[\sqrt[3]{0} = 0\].

And the cube of \[1\] is \[1 \times 1 \times 1 = 1\] and cube root of \[1\] is \[\sqrt[3]{1} = 1\]

Therefore, the numbers \[0,1\] have the same cube and cube roots.

Thus, the correct options are A. \[ - 1,1\] and D. \[0,1\].

Note: In this problem you have to choose all the correct options. And it is not necessary to write the exact value of the cube root number, you can make them up to three decimal points. If one of the numbers in the option satisfies the conditions given in the problem and another number is not satisfied then that option is considered as an incorrect option.

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