Question

What will be the unit digit of the square of $3853$?
1). $3$
2). $1$
3). $7$
4). $9$

Answer 1

Hint: First, we need to know about the concept of the square root. The square root of the number is a value, which on multiplied by itself given the original number, which is the given numbers that obtain by multiplying any of the whole numbers (zero to infinity) twice, or the square of the given numbers yields a whole number like \[\sqrt 9 = {\sqrt 3 ^2} = 3\] and the square is ${3^2} = 3 \times 3 = 9$. The square and square roots are inverse processes and also called the perfect square if both are satisfied.

Complete step-by-step solution:
Since from given we need to find the unit digit of the square of $3853$
We also need to know about the concept of face value. The face value of a digit describes the value of the digit itself. It does not depend on which position or place of the digit in a number
Hence the unit value means the last digit of the given number.
Thus, we have the unit digit $3$ for $3853$
Now we will multiply the number $3$ to itself to get the square of the value, hence we have ${3^2} = 3 \times 3 = 9$
Therefore, the unit digit is $9$
We can also able to take the square of the given number, which is ${3853^2} = 14845609$ and we got the same unit digit as $9$ (long process)
Hence the option 4) $9$ is correct.

Note: Clearly we see that the last digit square does not change the resultant.
The place value describes the position or place of a digit in a number. each of the digits of the number has a value depending on its place. Place value of the digit can be calculated by the face value times of the numerical value of the place.
Hence the place of $729$ can be expressed as
Place of the third digit $9 = 9$
Place value of the second digit $2 = 2 \times 10$
Place value of the unit digit $7 = 7 \times 100$