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