Question

The cube of a single digit number may be a ________ digit number.
A. Single
B. Double
C. Three
D. All of these

Answer 1

Hint: We know that single digit numbers are 0, 1, 2, 3 . . . . 9. Also, the cube of a number means the number multiplied by itself 3 times. If we have \[{a^3}\] then,
\[{a^3} = a \times a \times a\]
So, we will find the cube of a number between 0 to 9 and then, we will find the required value.

Complete step by step solution:
We have been asked to find the cube of a single digit number containing how many digits.
We have single digit numbers 0, 1, 2, 3 . . . . . . 9.
We know that the cube of a number means the number multiplied by itself three times. If we have \[{x^3}\] then,
\[{x^3} = x \times x \times x\]
Now, we will find the cube of numbers from 0 to 9 as follows:
\[{0^3} = 0 \times 0 \times 0 = 0\]
It is a single digit number.
\[{1^3} = 1 \times 1 \times 1 = 1\]
It is a single digit number.
\[{2^3} = 2 \times 2 \times 2 = 8\]
It is a single digit number.
\[{3^3} = 3 \times 3 \times 3 = 27\]
It is a two digit number.
\[{4^3} = 4 \times 4 \times 4 = 64\]
It is also a two digit number.
\[{5^3} = 5 \times 5 \times 5 = 125\]
It is a three digit number.
\[{6^3} = 6 \times 6 \times 6 = 216\]
It is also a three digit number.
\[{7^3} = 7 \times 7 \times 7 = 343\]
It is also a three digit number.
\[{8^3} = 8 \times 8 \times 8 = 512\]
It is also a three digit number.
\[{9^3} = 9 \times 9 \times 9 = 729\]

It is also a three digit number.

Hence, the cube of a single digit number may be a single, double and three digit number.
Therefore, the correct option is D.

Note: You can also remember the point that a cube of any number \[{a^3}\] contains a maximum digit number equal to the product of 3 and the digit of the number is perfect. There is a great possibility that the student might choose option C. Three as the right answer using logic that the cube of a single digit number is essentially multiplying that number three times with itself. So, it will be a three digit number. But, this is just illogical. It is necessary to get the final result of multiplication of that number three times and then come to a conclusion. So, the best way is to check the cube of the smallest and largest single digit number, i.e 0 and 9. Cube of 0 is a single digit number and cube of 9 is a three digit number, so definitely, options A, B, C are correct.