Some facts about square numbers and their roots.

Squares and roots 

When a number or integer (not a fraction) is multiplied by itself, the resultant is called a 'Square Number'. For example, 3 multiplied by 3 is equal to 3-squared or 3 x 3 = 32.

Some interesting facts 


This particular collection of numbers are called square numbers (or squared numbers) for the simple reason that they form the area of a square. As squares have equal sides, finding the area is simple – just “square” (multiply by itself) one of its sides!




As we know that all the perfect square number ends with  1,4,9,6,5,0.

So, a number having 2,3,7 or 8 at unit's place is never a perfect square.

1. The square numbers end in 0, 1, 4, 5, 6 or 9 only.

2. If a number ends with 1 or 9, its square ends with 1.

3. If a number ends with 2 or 8, its square ends with 4.

4. If a number ends with 3 or 7, its square ends with 9.

5. If a number ends with 4 or 6, its square ends with 6.

6. If a number ends with 5 or 0, its square also ends with 5 or 0, respectively.

7. Square of an odd number is always odd, and the square of an even number is always even.
Can you guess what will happen if a squared number has zero in the unit's place?
 
Let's see few examples:
 
102=10×10=100
502=50×50=2500
902=90×90=8100
 
From the above examples, we can see that if the number with one zero in the unit's place is squared, then the square number will have two zeros.
 
Similarly, if the number has two zeros, then the square number will have four zeros.

Properties regarding Unit Digit of Perfect Square

Squares: There is a definite relationship between the unit digits when square of a number is considered, we will see that one by one.

– If unit digit of a perfect square is 1 then ten’s digit has to be Even
E.g. 81, 121, 441, 961 all are Perfect Square having unit digit 1 and tens digit is even.

– If unit digit of a number is 2 then it can’t be a perfect square.

– If unit digit of a number is 3 then it can’t be a perfect square.

– If unit digit of a perfect square is 4 then ten’s digit has to be Even.

E.g. 64, 144, 484 all are Perfect Square having unit digit 4 and tens digit is even.

– If unit digit of a perfect square is 5 then ten’s digit has to be 2.

E.g. 25, 225, 625,1225 all are Perfect Square having unit digit 5 and tens digit is 2.

– If unit digit of a perfect square is 6 then ten’s digit has to be Odd. e.g. 256, 576, 676, 1296 etc.

– If unit digit of a number is 7 & 8 then it can’t be a perfect square

– If unit digit of a perfect square is 9 then ten’s digit has to be Even.

E.g. 49, 169, 529 all are Perfect Square having unit digit 9 and tens digit is even.

– If unit digit of a perfect square is 0 then ten’s digit has to be 0.
E.g. 100,400,900 all are Perfect Square having unit digit 0 and tens digit is 0.

If a number ends with 2, 3, 7 or 8 then it can’t be perfect square.

-Square of any natural number has last two digits same as that of last two digits of squares of first twenty–five natural numbers. For example if we calculate square of
88 we get 7744. You can notice that last two digits are 44, which are same as last two digits of the square of 12 i.e. 144.

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