How do you find the square root of 3481?

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Answer 1 · 2017-02-07T19:59:27

#sqrt(3481) = 59#

Normally when faced with a large number to find the square root of you would see what prime factors it has.

#3481# has no small prime factors, so let's try another approach...

Split it into pairs of digits starting from the right to get:

#34"|"81#

Looking at the most significant pair of digits, what is the square root of #34#?

We know #6^2 = 36#, so it's a little less than #6#.

Hence #sqrt(3481)# is a little less than #60#.

Let us try #59^2#...

#59^2 = (60-1)^2=60^2-2*60+1 = 3600-120+1 = 3481#

So:

#sqrt(3481) = 59#