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:

$sqrt(3481) = 59$