# sqrt167 lies between which two successive integers?

Mar 1, 2017

12 and 13

#### Explanation:

Let $n$ be the lower of the successive integers.

Thus: $n < \sqrt{167} < \left(n + 1\right)$ $\left[n \in \mathbb{Z}\right]$

$\sqrt{167} \cong 12.9228$

$\therefore n =$the interger part of $12.9338 = 12$

Hence: $12 < \sqrt{167} < 13$

To check this result:

Consider ${12}^{2} = 144$ and ${13}^{2} = 169$

and $144 < 167 < 169$