Question

what is an irrational number between 5.2 and 5.5?

Answer 1

$5.2 \ \textless \ x \ \textless \ 5.5 \\ \\ \sqrt{5.2^2} \ \textless \ \sqrt{x^2} \ \textless \ \sqrt{5.5^2} \\ \\ \sqrt{27.04} \ \textless \ \sqrt{x^2} \ \textless \ \sqrt{30.25}$

Let x^2 be any whole number between 27.04 and 30.25.

$x^2 = 29 \\ \\ x = \sqrt{29}$