Question

If the unit digit of a cube of a number is \[6\], then what is the unit digit of the number?
A). \[2\]
B). \[4\]
C). \[6\]
D). \[8\]

Answer 1

Hint: In the given question, we have been given that there is a cube whose unit digit is given. We have to find the unit digit of the number. To solve that, we are going to write the cube of the even numbers till ten, not their unit digits and then choose the appropriate option from the given choice.

Formula used:
The cube of a number \[x\] is given by,
Cube \[ = \left( x \right) \times \left( x \right) \times \left( x \right) = {\left( x \right)^3}\]

Complete step by step solution:
First, the word “cube” means the product of a number three times with itself.
So, let us find the cubes of the even numbers till ten.
\[{2^3} = 2 \times 2 \times 2 = 8\]
So, this does not match the condition.
\[{4^3} = 4 \times 4 \times 4 = 64\]
This too does not match the condition.
\[{6^3} = 6 \times 6 \times 6 = 216\]
Hence, this matches the condition.
So, the unit digit of a number whose cube ends with a \[6\] is also a \[6\].
Thus, the correct option is C.

Note: In the given question, we were given the unit digit of a cube. We had to find the unit digit of its cube root. We solved it by writing the cube of the even numbers till ten, noted their digits and then chose the one matching the given condition. We just need to know the meaning of the word “cube” and everything else was pretty easy.