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What are the numbers which cannot come to the unit place of a perfect square?

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Numbers that Cannot come at the Unit Place of any Perfect square are 2, 3, 7, and 8.

A square number or perfect square is an integer resulting from multiplying an integer by itself. It’s the product of an integer with itself. For example, 25 qualifies as a square number because it equals 5², which is equivalent to 5 multiplied by 5.

Example: Perfect Square of Numbers from 1 to 10.

Integers

Perfect Squares

1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100

It is evident from this list that the unit digits of perfect squares are consistently 0, 1, 4, 5, 6, or 9. These numbers appear repeatedly in every perfect square.

Some more Examples include:

Number

Square

Number

Square

11

121

106

11236

12

144

117

13689

13

169

199

39601

14

196

200

40000

15

225

218

47524

From above we can concluded that, 0, 1, 4, 5, 6, or 9 are the Unit Place of perfect square, so all the digits, except 0, 1, 4, 5, 6, or 9, are the digits that cannot come at Unit Place of a Perfect Square.

So, Numbers that Cannot come at Unit Place of a Perfect square are: 2, 3, 7 and 8.

Let’s take some example for the same:

  • Check if the number 4568 is perfect square.

Ans. No, its not, as the unit place is ‘8’, and a perfect square can never have numbers 2,3,7 and 8, at unit place.

  • Check if the number 232 is perfect square.

No, its not, as the unit place is ‘2’, and a perfect square can never have numbers 2,3,7 and 8, at unit place.

Conclusion:

Perfect squares offer important insights into the characteristics of numbers by displaying intriguing patterns in their unit digits. It is clear from looking at the squares of the numbers 0 through 9 that perfect squares always finish in one of the following: 0, 1, 4, 5, 6, or 9.

Numbers ending in 2, 3, 7, or 8 cannot be the unit place of a perfect square because their squares end in different digits, as demonstrated by examples and analysis.

Recognizing these patterns improves our understanding of arithmetic and number theory, which helps us solve problems more quickly and develops a deeper appreciation for mathematics.

Related Articles

Even Numbers

Natural Numbers

Odd Numbers

Whole Numbers


Last Updated : 28 Mar, 2024
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