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. The ratio of their sides are : | |||
| Right Option : C | |||
| View Explanation | |||
From the following options choose which natural number is a perfect square. | |||
| Right Option : D | |||
| View Explanation | |||
A teacher arranges his students in such a way that each row contains as many students as there are rows. If in each row there are 80 students, and 20 students remained in the end what was the total number of students ? | |||
| Right Option : D | |||
| View Explanation | |||
Students / Parents Reviews [10]
About 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 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
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
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 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
10thBeing 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
8thA 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
7thAbhyas 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
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
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
