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.