Mathematics
Grade-8
Easy

Question

How many two-digit numbers satisfy this property. : The last digit (unit's digit) of the square of the two-digit number is 8?

  1. 1
  2. 2
  3. 3
  4. None of these

hintHint:

Last digit of square of a number = (last digit of the number)2

The correct answer is: None of these


    GIVEN CONDITION-
    Unit's digit of the square of a 2 digit number = 8
    TO FIND-
    Numbers that satisfy the given condition.
    SOLUTION-
    We know that-
    Last digit of square of a number = (last digit of the number)2
    Last digit of any number (digit at unit's place) will be either of the following- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, whose squares are- 0, 1, 4, 9, 16, 25, 36, 49, 64, 81.
    Hence, we can conclude that square of any given number can never end with 2, 3, 7 and 8 as the digit at unit's place.
    FINAL ANSWER-
    Option 'c' i.e. 'None of these' is the correct answer to the given question.
    A number ending in 8 can never be a perfect square.

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