Question

The number \[x\]which multiplied by itself three times gives a cube number \[y\]. Then \[x\] is a \[\_\_\_\_\] of \[y\].
\[\begin{align}
  & \text{A}\text{.cube root} \\
 & \text{B}\text{.square root} \\
 & \text{C}\text{.cube} \\
 & \text{D}\text{.none of these} \\
\end{align}\]

Answer 1

Hint: We know that when a number is multiplied twice, the obtained number is termed as square of the number multiplied and the number being multiplied is called as square root of the obtained number. In the same way, we must find out what the number is called when it is being multiplied thrice.

Complete step by step answer:
Now let us learn about cubes and cube roots. All the numbers in the number system have cubes but all the numbers do not have cube roots as whole numbers. A natural number is said to be a perfect cube only if it is the cube of a natural number. In order to check if a number is a perfect cube, we can test if the number is divisible by any of the prime numbers. If the prime number divides the number, then we say that the cube of this prime number also divides the number. From this, hence we can conclude that the number is a perfect cube.
Now let us find what is \[x\] of \[y\].
So when a number \[x\] is multiplied to itself three times, we obtain the cube of the number \[x\] and it is said to be \[y\]. With respect to \[y\], \[x\] is called as the cube root of \[y\].

So, the correct answer is “Option A”.

Note: We must always have a note that the cube of a negative number will always be negative. And also the same with the cube root in case of a negative number. Also we can compute the cube root if we check that the cube root of the product of two perfect cubes is the product of their cube roots.