Question

Is the value of $\sqrt{42}$ a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?

Answer 1

$\bf \sqrt{42}\qquad \boxed{42=2\cdot 3\cdot 7}\implies \sqrt{2\cdot 3\cdot 7}\implies \sqrt{2}\cdot \sqrt{3}\cdot \sqrt{7}$

now, all those three factors are all irrationals. thus their product is also irrational.


$\bf \sqrt{42}\approx 6.48 \qquad\qquad \boxed{5}------6--6.48---\boxed{7}$