# How do you find the square root of 6889?

##### 1 Answer

#### Explanation:

Note that

In our example, we only need to divide

Hopefully we know the first

#8^2 = 64 < 68.89 < 81 = 9^2#

Hence:

#8 < sqrt(68.89) < 9#

and:

#80 < sqrt(6889) < 90#

We can linearly interpolate to get closer.

Linearly interpolating in this way is approximating part of the parabola of

#sqrt(6889) ~~ 80 + (6889-80^2)/(90^2-80^2)*(90-80)#

#=80 + (6889-6400)/(8100-6400)*(90-80)#

#=80+4890/1700#

#~~82.88#

Hmmm. That's quite close to

#83^2 = 6889#

So:

#sqrt(6889) = 83#