Properties of Square - Based on Pattern
Properties of Square - Based on Pattern
A pattern refers to a series or sequence which repeats. There are two major kinds of math patterns. They are number patterns or sequences of numbers. These are arranged as per a rule or rules or a formula. The other type we have are shape patterns that are tagged by making use of letters in a definite shape and the way that they repeat.
Some interesting patterns of square numbers :
Pattern 1:The sum of two consecutive triangular numbers is a square number .
Numbers whose dot patterns can be arranged as triangles are known as triangular numbers.1,3,6,10,15,21,... are triangular numbers.This fact can be observed by the following pattern
etc.
Also nth triangular number is given by
Pattern 2: If 1 is added to the product of two consecutive odd natural numbers,it is equal to the square of the only even natural number between them.
This fact can be observed by the following pattern
etc.
In general,
Pattern 3: If 1 is added to the product of two consecutive even natural numbers,it is equal to the square of the only odd natural number between them.
This fact can be observed by the following pattern
etc.
In general:
Pattern 4:The square of any odd natural number other than 1 can be expressed as the sum of two consecutive natural numbers.
Express | |||
| Right Option : B | |||
| View Explanation | |||
Observe the following pattern and find the value of | |||
| Right Option : C | |||
| View Explanation | |||
Which of the following statements are false 1. The number of digits in a square number is even. 2. The square of a prime number is prime 3. No square number is negative. 4. The sum of two square numbers is a square number. | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas 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
10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thAbhyas 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
10thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
Sharandeep Singh
7thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thIt 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
10thIt 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 with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
Ayan Ghosh
8thAbhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
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
10thMy 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.
