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CBSE Class 10 Answered

how can we find the square root of a large number quickly?
Asked by | 18 Feb, 2013, 06:05: PM
answered-by-expert Expert Answer
There are a number of methods to find the square root of a number, which one to use is dependent on the nature and how large the number is. 
 
1. Factorization - Probably the most easiest method. If you have a 3-4 digit number, I would recommend you to write down its factors and use that to find its root. 
 
2. Learn the squares of all numbers from 1 - 30 and so, if you number is <900, then you can easily write down its root. For numbers greater than that, you can figure out between what (like 30-40 or 40-50 and so on..) will your root lies by checking if your number lies between 900 and 1600 for 30-40 range or between 1600 - 2500 for 40-50 range and so on..
 
3. The most elegant and proper way of calculating square roots for large numbers is to use the divide the number into pairs of 2 digits starting from the decimal point and then using quotient and remainder to find the root (called the duplex method or the long method for finding square root). I guess this method is usually taught in class 8th. 
 
4. Sometimes, you could use identities like a2 -b2 or (a+b)2  or (a-b)2 to define your number as the sum of squares of 2 other numbers whose root you know and use the identity to find what could be the root of the your number. 
Answered by | 18 Feb, 2013, 06:34: PM

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