Question

The unit digit in the cube of the number 50 is
(a)1
(b)0
(c)5
(d)4

Answer 1

Hint – There can be two ways to solve this problem first will be using the concept that 50 is written as $\left( {5 \times 10} \right)$, so ${(50)^3}$ can be written as ${\left( {5 \times 10} \right)^3}$, then solve this to get the unit digit in the cube of the number. The second method is a tricky method to find the cube of any number so we will discuss it in the ending of the solution.

Complete step-by-step answer:
Consider a number abcxyz in this number z place is called as once or unit place, y place is called as ten place, x place is called as hundreds place, c place is called as thousand place and so on...
Now we have to find out the unit digit or unit place in the cube of the number 50.
Let the cube of the number 50 be P.
Therefore, P = ${\left( {50} \right)^3}$
Now as we know 50 is written as $\left( {5 \times 10} \right)$
Therefore, P = ${\left( {5 \times 10} \right)^3}$
$ \Rightarrow P = {5^3} \times {10^3}$
Now as we know that the cube of 5 (i.e. ${5}^{3}$) is 125 and the cube of 10 (i.e. ${10}^{3}$) is 1000.
So the value of P is
$ \Rightarrow P = 125\left( {1000} \right) = 125000$
So this is the cube of the number 50.
Now as we see that in 125000 the unit, ten and hundred place or digit is same (i.e. zero).
So the unit digit of the cube of the number 50 is zero (0).
So this is the required answer.
Hence option (B) is the correct answer.

Note – So, the trick part to find the cube of any number is comprised of three basic steps let’s take the given number as 50 and we have to find the cube of this number, so firstly consider 4 blank spaces beneath the number like

Now to the left most blank space write the cube of the leftmost digit of the number whose cube is to be taken out and fill the right most blank with the cube of the rightmost digit of the number whose cube is to be taken out like

Now to the second blank space from the left put the square of the leftmost digit multiplied with the rightmost digit that is, fill the second blank from left with ${(5)^2} \times 0$ and to the second blank space from the right put the square of the leftmost digit multiplied with the square of the rightmost digit that is fill the second blank space from the right with$5 \times {(0)^2}$. So it looks like now

Now for the middle terms write the double of their magnitude just beneath them that is

Now add everything that is

 Keep a note of one thing this is not the answer although in the case of cube of 50 125000 is the answer. If the added number has more than one digit then to find the answer take the unit most digit of the left most added space and then carry forward this carry to the next space added answer then again take only the unit place number and again carry forward the carry. Take the entire last number that is the right most space comprising all the unit digits numbers taken will form the answer.
Example in case of cube 23 that is ${(23)^3}$ talking about the last step we have

So the answer is 12167 for the cube of 23.