Properties of Square - Based on Ending Digits


 
 
Concept Explanation
 

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.

 

Number

Square of Number

Odd/Even

Number

Square of Number

Odd/Even

0

02 = 0

Even 1

12 = 1

Odd
2

22 = 4

Even 3

32 = 9

Odd
4

42 = 16

Even 5

52 = 25

Odd
6

62 = 36

Even 7

72 = 49

Odd
8

82 = 64

Even 9

92 = 81

Odd
10

102 = 100

Even 11

112 = 121

Odd
12 122 = 144 Even 13 132 = 169 Odd
14 142 = 196 Even 15

152 = 225

Odd
16

162 = 256

Even 17

172 = 289

Odd
18 182 = 324 Even 19 192 = 361 Odd
20 202 = 400 Even      
 
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Sample Questions
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Question : 1

Which of the following number is a perfect square ?

Right Option : D
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Explanation
Question : 2

Which of the following is not a perfect square ?

Right Option : C
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Explanation
Question : 3

What could be the possible "one's digit" of the square root of 625?

Right Option : A
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Explanation
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