How do you find the square root of 3481?

Feb 7, 2017

$\sqrt{3481} = 59$

Explanation:

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:

$34 \text{|} 81$

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 ${59}^{2}$...

${59}^{2} = {\left(60 - 1\right)}^{2} = {60}^{2} - 2 \cdot 60 + 1 = 3600 - 120 + 1 = 3481$

So:

$\sqrt{3481} = 59$