# How do you simplify sqrt(6889)?

Apr 1, 2016

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 $6889$.

• ${80}^{2} = 6400$
• ${81}^{2} = 80 \cdot 80 + \textcolor{h i g h l i g h t}{81 + 80} = 6400 + \textcolor{g r e e n}{161} = 6561$
• ${82}^{2} = 81 \cdot 81 + \textcolor{h i g h l i g h t}{82 + 81} = 6561 + \textcolor{g r e e n}{163} = 6724$
• ${83}^{2} = 82 \cdot 82 + \textcolor{h i g h l i g h t}{83 + 82} = 6724 + \textcolor{g r e e n}{165} = 6889$

Well... there you have it.

$\textcolor{b l u e}{\sqrt{6889} = \pm 83}$.