Perfect Square
Perfect Square
Square of a number and square numbers:
The square of a number is that number raised to the power 2.
Thus, if a is a number, then the square of a is written as and is given by
That is, the square of a number is obtained by multiplying it by itself
If i.e.
, then we say that the square of number a is number b or the number b is the square of number a.
For example,
so we say that the square of 2 is 4
so we say that the square of 3 is 9
so we say that the square of 12 is 144 etc.
Perfect Square or Square Number:
A natural number n is called a perfect square or a square number if there exist a natural number m such that
In other words, a natural number is a perfect square if it is the square of the same natural number.
Since Therefore, 4 is a square number.
Also,
so 25 is a square number or a perfect square.
so 144 is a square number or a perfect square etc.
STEP I Obtain the natural number.
STEP-II Write the number as a product of prime factors.
STEP III Group the factors in pairs in such a way that both the factors in each pair are equal.
STEP IV See whether some factor is leftover or not. If no factor is left over in grouping, then the given number is a perfect square. Otherwise, it is not a perfect square.
STEP V To obtain the number whose square is the given number take one factor from each group and multiply them.
Illustration: Show that 17640 is not a perfect square.
Solution: Resolving 17640 into prime factors, we have
The area of two square fields are respectively 256 and 625 square meters. If both the squares are made into a new square field,then the area will be ____________ | |||
| Right Option : B | |||
| View Explanation | |||
The smallest number by which 136 must be multiplied so that it becomes a perfect square is __________________. | |||
| Right Option : C | |||
| View Explanation | |||
The perfect square number between 30 and 40 is: | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
My 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 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 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
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
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
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thMy 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
7thWhen 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
7thI 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 with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thMy 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
8thBeing 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
8thIt 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
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
7thAbout 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
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
7thThe 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
10thIn 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
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.
