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.
256 can be express as the sum of first ___________________ consecutive odd numbers. | |||
| Right Option : D | |||
| View Explanation | |||
Find the square of -15. | |||
| Right Option : B | |||
| View Explanation | |||
The sum 1 + 3 + 5 + 7 + 9 is _________________ .
| |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [10]
Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
