Question

State true or false: The cube of a two-digit number may be a three-digit number.
${\text{A}}{\text{.}}$True
${\text{B}}{\text{.}}$False

Answer 1

Hint: Think about the cube of the smallest two-digit number, i.e. cube of 10 is 1000, which is a four-digit number.

Complete step-by-step answer:

The given statement is False. Here is the explanation with an example.
Let us take the smallest two-digit number, i.e. 10 and find the cube of it.
\[{(10)^3} = 1000\]

So, if the cube of the smallest two-digit number is a four-digit number, i.e. 1000, then we can
say that the cube of all two-digit numbers will be greater than or equal to the cube of 10, which is 1000, a four-digit number.

Hence, the above statement given in the question i.e., the cube of two-digit number may be a three-digit number is false.

Note: For such types of questions, always see the boundary condition, i.e. cube of smallest or largest two-digit number (as given in question). Cube of all two-digit numbers will be greater than or equal to the cube of 10.