How to find a perfect square?

HOW CAN YOU GET TO KNOW , WHICH NUMBER IS A PERFECT SQUARE?

You'll often find questions like these in the teacher eligibility test examinations.A lot of students puzzle over how to find a perfect square..And it is really easy to check which of the following number is a perfect square.

How to find a perfect square?

what is a perfect square?

any number which can be expressed as product of two integers is known as a perfect square.
e.g 25 can be expressed as 5x5, so it is a perfect square
100=10x10, so 100 is also a perfect square
but 80 can't be expressed like this, so it is not a perfect square. 


 How to check whether a number is a perfect square or not.?

1.All squares end up in 0,1,4,9,6,5

A perfect square never ends up in 2,3,7,8

So something like 15623 is not a perfect square , since it ends in 3...

And you don't have to cram it..Just check the unit digit of squares of numbers 0-9

0x0=0
1x1=1
2x2=4
3x3=9
4x4=6
5x5=5
6x6=6
7x7=9
8x8=4
9x9=1

So as you can see, a perfect square Never ends in 2,3,7,8.This should be the first thing you should check ,while inspecting a number.

2.THE DIGITAL SUM OF A PERFECT SQUARE IS 1,4,7,9

MNEMONIC(1947)

Digital sum is the sum we get after adding all the digits of a number until we get a single digit.

E.g 15626=1+5+6+2+6=2+0=2

Since it's digital sum is 2, it can't be a perfect square for sure..

KEEP IN MIND, THAT IF THE DIGITAL SUM OF A NUMBER IS 1,4,9,7, IT DOESN'T GUARANTEE THAT THE NUMBER IS A PERFECT SQUARE...

BUT IF THE DIGITAL SUM ISN'T 1,4,7,9, THEN THE NUMBERS CANT BE A PERFECT SQUARE FOR SURE..

SO IT IS AN ELIMINATION METHOD...

3.SOME OTHER THINGS TO CHECK

●If a number ends in 1, then tens digit is always even.

E.g 121, 961

●If a number ends in a 9, it's tens digit is always even

E.g 169,529

●If a number is ends in 5, then it's tens digit is always 2..

E.g 625, 5625

●If a number is even, then it's last two digits are divisible by 4

E.g. 64,144,196,8464

So if any of the above rules fail, then the number can't be a perfect square

E.g

34531(it ends in 1, and the ten's place isnt even, so it cant be a perfect square)

139(it ends in 9, and tens digit is odd, so it can't be a perfect square)

4575 (it ends in 5, and the tens digit is other than 2, so it is not a perfect square)

1214 ( it ends in 4, and last two digits are not divisor by 2, so it is not a perfect square)

Using these tricks , you can  eliminate the numbers which are not perfect squares, and get to know the answer..

Question 1:-
Which of the following is a perfect square

A..548543213
B..548543215
C..548543251
D..548543241

◆digital sum of option a is 8, So it can't be a perfect square

◆Option b, ends in 5 and has an odd digit on tens place , so it can't be a perfect square

◆In option c , the number ends in 1 and the tens digit is odd, which is not possible in case of a perfect square

◆So our answer is option D