# Show the steps of square rootof 6889 ?

Aug 6, 2018

The square root of $64$ is $8$, so the square root of $6400$ is $80$. That means the square root of $6889$ is larger than $80$.

The number ends in a $9$, so the square root, if it is a whole number, ends in $3$. Therefore, my first guess is $83$.

$\sqrt{6889} = 83$?

So let's try to work backwards to verify.

$83 \times 83$

$= 80 \times 80 + 3 \times 83 + 80 \times 3$

$= 6400 + 249 + 240$

$= 6889$ color(blue)(sqrt"")