The number whose cube and cube root both are equal is ……………………….
This question has multiple correct options
A. \[ - 1,1\]
B. \[2, - 2\]
C. \[1,2\]
D. \[0,1\]
Last updated date: 24th Mar 2023
•
Total views: 308.1k
•
Views today: 4.85k
Answer
308.1k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
