Is the value of √(42) a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?

Question

Is the value of
`√(42)` a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?

Answer 1

`\bf √(42)\qquad \boxed{42=2\cdot 3\cdot 7}\implies √(2\cdot 3\cdot 7)\implies √(2)\cdot √(3)\cdot √(7)`

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



`\bf √(42)\approx 6.48 \qquad\qquad \boxed{5}------6--6.48---\boxed{7}`