Which of the following is an irrational number between 5 and 7: 6–√ , 12−−√ , 27−−√ , 36−−√ ?

Answer 1

To determine which of these numbers are irrational, we need to find the square root of each one:

$6-\sqrt{} \approx -0.4$
$12-\sqrt{} \approx 2.9$
$27-\sqrt{} \approx 4.2$
$36-\sqrt{} \approx 5.9$

The only number that does not simplify to a rational number when taking its square root is $\boxed{27-\sqrt{}}$.