Properties of Square - Based on Ending Digits
Properties of Square - Based on Ending Digits
Property 1
A number having 2, 3, 7 or 8 at units place is never a perfect square. In other words, no square number ends in 2, 3, 7 or 8.
Application: Check the digit at units place of the given number. If it is one of the digit 2, 3, 7 and 8, then the given number is not a perfect square.
Illustration: None of the numbers 152, 7693, 14357, 88888, 798328 is a perfect square.
Property 2:
The number of zeros at the end of a perfect square is always even.
In other words, a number ending in an odd number of zeros is never a perfect square.
Verification: Consider the following tables:
| Number | Number of zeros at units place | Square of the number | Number of zeros at the units place of the square number |
| 10 | 1 | 100 | 2 |
| 20 | 1 | 400 | 2 |
| 200 | 2 | 40000 | 4 |
| 2500 | 2 | 6250000 | 4 |
| 5000 | 3 | 25000000 | 6 |
| 20000 | 4 | 400000000 | 8 |
Remark: It should be noted that number which ends in an odd number of zeros , we can not be a perfect square. For example, 2500 is a perfect square but, 2600, 44700 etc. are not perfect squares.
Property 3:
Squares of even numbers are always even numbers and squares of odd numbers are always odd numbers.
Verification: This fact can be easily verified by analysing the squares of natural numbers upto 15. However, the result is true in general.
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The square of which of the following would be even number? | |||
| Right Option : A | |||
| View Explanation | |||
758 is a perfect square of which natural number ? | |||
| Right Option : D | |||
| View Explanation | |||
The square of which of the following would be odd number? | |||
| Right Option : A | |||
| View Explanation | |||
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