Question

" If a square root is not a perfect square, then it is considered as an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating)." stated by books and online.

But there are many times that a root of a non perfectly square need not to be irrational
For example
Root of 1.69
It is impossible for it to be a perfect square because it have some decimals. it is a irrational number stated above, but the truth is that root 1.69= 1.3 which for hundred percent to be a rational number.
So that I want to ask, is all the unperfect square truly irrational?

Answer 1

Yes, all unperfect square are truely irrational.
but in your question
$\sqrt{1.69 }$
$= \sqrt{169 \div 100}$
$= 13 \div 10$
=1.3