1. The square of any natural number will end in 0, 1, 4, 6, or 9. It cannot end in 2, 3, 7, or 8. 2. If a number ends in 0, its square will end in an even number of zeros. If it ends in an odd number of zeros, it cannot be a perfect square. 3. If a number ends in 5, its square will also end in 5.

1. PROPERTIES OF
SQUARE NUMBERS

2. if we analyse the table of squares of the first 100 natural numbers, we
observe that every square number (example value of and N 2 )and with any
one of the digits 0 ,1, 4 ,5 ,6 or 9
in other words a square number cannot have its and digits as 2,3,7 or 8
example 352,433,527 and 118 cannot be perfect square.
PROPERTIES OF SQUARE NUMBERS

3. study the table of squares of natural numbers we observed that;
1 2 =1 29 2 =841
9 2 =81 21 2 =441
11 2 =121 19 2 =361
(example) if a number has one or 9 in the units place then its square has
one unit in the place
2 PROPERTY OF SQUARE NUMBERS

4. studying the table of squares of natural numbers we observed that
4 2 = 16; 6 2 =36; 14 2 =196; 16 2=256
example if a number has 4 or 6 in the in the units place then its square has
6 in its units place
3. Property of squares

5. from tables of squares we also observed that;
3 2=9; 7 2 =49 13 2 = 169; 17 2 = 289
example ‘if a number has 3 or 7 in the units place, then its square has 9 in
its unit place.’
4 property

6. we have
10 2 = 100; 20 2 =400 100 2 =10000; 200 2 = 40000
example if a number has one zero at its end,its a square has two zeros at
the end, and if a number has two zeros at its end, then its square has four
zeros at the end.thus we can say that
‘if a number has m zeros at its end,then its square has 2m zeros at the end’.
in other words- ‘a square number can have only even number of zeros at its
end’.
5 property
A number ending with odd
number of zeros can never be
a perfect square.

7. square of an even number is always even and square of an
odd number is always odd
for example: 2 2=4; 5 2 =25; 3 2 = 9; 8 2 =64
6 property
A number ending with even
number of zeros need not be a
perfect square. For
example:1200 has two zero at
its end,but it is not square
number

8. if a number and with digit 5 its square also ends with digit 5
for example: 15 2 = 225 35 2= 1225; 95 2 = 9025
8th property; perfect squares always positive.
For example;
(-3) 2= 9; 3 2 = 9; (-12 ) 2 =144; 12 2 =144
7th property

9. Q .Perfect_____ are always ______.
Q.. if a number ends with digit ___, its square also ends with digit ____.
Q. ONLY ONE NUMBER OUT OF THE FOLLOWING NUMBERS IS NOT A
SQUARE CAN YOU IDENTIFY THAT NUMBER?? 225,400,627,144,196
Q. is it possible that 139 × 139 =19,321
Q which among 23 2, 17 2,32 2,54 2 ,109 2 would end with digit 6??
questions

10. 1. Squares , positive.
2. 5,5
3. as a perfect square cannot end with number 2,3,7 or 8, therefore 627
cannot be a perfect square.
4. Yes it is possible, as the square of 9 ends with 1.
5. We know that square of a number ends with digits 6, only if the end
digit of the number is 4 or 6 . therefore 54 2 will end with digit 6
answers