$sqrt167$ lies between which two successive integers?

Question

2348 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-01T05:45:24

12 and 13

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

Thus: $n< sqrt167<(n+1)$ $[n in ZZ]$

$sqrt167 ~= 12.9228$

$:. n =$ the interger part of $12.9338 = 12$

Hence: $12< sqrt167<13$

To check this result:

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

and $144<167<169$

sqrt167sqrt167 lies between which two successive integers?