The square numbers are the values which are produced when we multiply a number by itself. Some of the properties are:
In other words, a perfect square leaves remainder 0 or 1 on division by 3.
Verification: The above property can be easily verified from the following computations:
Square number | Remainder when divided by 3 |
1 | |
0 | |
1 | |
1 | |
0 | |
1 | |
1 |
Application: If a number when divided by 3 leaves remainder 2, then it is not a perfect square.
In other words, a perfect square leaves remainder 0 or 1 on division by 4.
We have,
Sum of first 1 odd natural number,
Sum of first 2 odd natural numbers,
Sum of first 3 odd natural numbers.
Sum of first 4 odd natural numbers.
25 can be express as the sum of first ___________________ consecutive odd numbers. | |||
Right Option : B | |||
View Explanation |
If a number has 1 or 9 in the unit’s place, then its square ends in ___________. | |||
Right Option : A | |||
View Explanation |
121 is the sum of n odd natural numbers where n is _______________. | |||
Right Option : B | |||
View Explanation |
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