Question

What will be the unit digit of the square of the number 26387?

Answer 1

Hint: Multiply the unit place digit of the given number by the digit itself and the number obtained at unit place will be the unit digit of the square of the given number.

Complete step-by-step answer:
Unit place digit is the rightmost digit of a given number. When a number is multiplied by the number itself then the process is called squaring of the given number. We can see that if any number, with any unit place digit is multiplied by the number itself then only some digits can appear at the unit place. Digits 0, 1, 4, 5, 6, 9 can only appear at the unit place when a number is squared, and digits 2, 3, 7, 8 never occur at the unit place. Now, when any number is squared then 0 will occur at the unit place when the last digit of the number which is being squared is also 0. Similarly, digit 1 will occur when there is 1 or 9 at the unit place of the squared number. Digit 4 occurs when the last digit of the squared number is 2 or 8. 5 appears when the last digit is 5. 6 appears for numbers containing 4 and 6 as its last digit and 9 appears when the number contains 3 or 7 at its unit place.

Now, we have been given the number 26387. It contains 7 at its unit place, so, the digit we will get when this number is squared is 9, because 7 multiplied by 7 is 49 and 4 will get carried over and 9 will remain at the unit place.

Note: The process of direct multiplying this given number with the number itself will be a lengthy and time consuming process. So, this short process is applied here. Further it was not necessary to square the given number to know its unit digit. One can only check by squaring the number that our answer is correct.