square root

Question

how to do big numbers square root?

Answer 1

Not sure what you mean exactly by "big numbers", but they square root the same way small numbers square root - by finding a number x such that x² is equal to the given number.  For example, the square root of 100 is 10 because 10² = 100.  The square root of 10,000 is 100 because 100² = 10,000.  Note that the principal square root is taken to be the one with x≥0, so the square root of 100 is +10 even though (-10)² is also equal to 100.  

 

If you have a number that is not a perfect square, like 360 for example, you can either use a calculator to get an approximate answer 

 

√360 ≅ 18.97  

 

or you can factor 360 to simplify the radical to get an exact answer  

 

360 = 2*180 = 2*(2*90) = 2*2*(2*45) = 2*2*2*(3*15) = 2*2*2*3*(3*5) = 2³*3²*5  so  

 

√360 = √(2²*2*3²*5) = √2² * √3² * √(2*5) = 2*3*√10 = 6√10  

 

If this doesn't answer your question then please add a comment or resubmit your question with a specific example of what you'd like to see