General Properties of Squares
General Properties of Squares
The square numbers are the values which are produced when we multiply a number by itself. Some of the properties are:
Property 1: The square of a natural number other than one is either a multiple of 3 or exceeds a multiple of 3 by 1.
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.
Property 2: The square of a natural number other than one is either a multiple of 4 or exceeds a multiple of 4 by 1.
In other words, a perfect square leaves remainder 0 or 1 on division by 4.
Property 3: The square of a natural number n is equal to the sum of first n odd natural numbers.
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.
Property 4 : The sum of first n odd natural numbers is 
i.e.
Check whether 563 is a perfect square of a natural number or not ? | |||
| Right Option : B | |||
| View Explanation | |||
Without adding,find the sum: 1+3+5+7+9+11+13+15+17+19+21+23 | |||
| Right Option : C | |||
| View Explanation | |||
25 can be express as the sum of first ___________________ consecutive odd numbers. | |||
| Right Option : B | |||
| View Explanation | |||
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8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
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