Question

How do you simplify `sqrt(6889)`?

Answer 1

We would try to find perfect squares that divide `6889`. If that is not possible, then consider `6889` as a perfect square. In that case, it can't be simplified under the square root.

Let's try starting at `80` as the square root, since it squares to get close to `6889`.

• `80^2 = 6400`
• `81^2 = 80*80 + color(highlight)(81 + 80) = 6400 + color(green)(161) = 6561`
• `82^2 = 81*81 + color(highlight)(82 + 81) = 6561 + color(green)(163) = 6724`
• `83^2 = 82*82 + color(highlight)(83 + 82) = 6724 + color(green)(165) = 6889`

Well... there you have it.

`color(blue)(sqrt(6889) = pm 83)`.