Square Root Using Prime Factorization
Square Root Using Prime Factorization
Square Root: The square root of a number a is that number which when multiplied by itself gives 'a' as the product.
Property: Negative numbers have no square root in the system of rational numbers.
Explanation:
We have, and so on.
Also,
and so on. This means that the square of a number whether positive or negative is always positive. Consequently, negative numbers are not perfect squares. Hence, negative have no square roots.
Square Root Of a Perfect Square By Prime Factorization
In order to find the square root of a perfect square by prime factorization, we follow the following steps.
STEP I Obtain the given number.
STEP II Resolve the given number into prime factors by successive division.
STEP III Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
STEP IV Take one factor from each pair.
STEP V Find the product of factors obtained in step IV.
STEP VI The product obtained in step V is the required square root.
The following examples will illustrate the above procedure.
Illustration 1: Find the square root of 7744 by prime factorization.
Class'X-A' of a school collected Rs.1024 As contribution to AP Flood Refief Fund . If each student contributed as one student in the class . The number of students in the class are _______________ | |||
| Right Option : B | |||
| View Explanation | |||
Find the smallest number by which 180 must be multiplied so that the product is a perfect square. | |||
| Right Option : C | |||
| View Explanation | |||
By which smallest number 90 must be multiplied so as to make it a perfect square? | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
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
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
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 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
8thI 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
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
10thAbhyas 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...
Aman Kumar Shrivastava
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
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8thThird 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
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Manya
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Manish Kumar
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Manish Kumar
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Ayan Ghosh
8thThe 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 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
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
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
10thMy 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
7thA 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.
